An angel is “a heavenly messenger who either delivers a message to humans, carries out God’s will, praises God, or guards God’s throne.” 
In the Bible the term ‘angel’ is used of an
- ordinary messenger (Job 1:14; 1 Samuel 11:3; Luke 7:24; Luke 9:52),
- of prophets (Isaiah 42:19; Haggai 1:13),
- of priests (Malachi 2:7,
- and ministers of the New Testament (Revelation 1:20).
It is also applied to such impersonal agents as
- the pestilence (2 Samuel 24:16-17; 2 Kings 19:35), and
- the wind (Psalms 104:4). 
The Holman Bible Dictionary explains:
The term “angel” is derived from the Greek word angelos which means “messenger.” Angelos and the Hebrew equivalent, malak (which also means “messenger”), are the two most common terms used to describe this class of beings in the Bible. In general, in texts where an angel appears, his task is to convey the message or do the will of the God who sent him. Since the focus of the text is on the message, the messenger is rarely described in detail.
Another set of terms used to describe angels focuses not on angels as mediators between God and persons, but on God’s heavenly entourage. Terms such as “sons of God,” “holy ones,” and “heavenly host” seem to focus on angels as celestial beings. As such, these variously worship God, attend God’s throne, or comprise God’s army. These terms are used typically in contexts emphasizing the grandeur, power, and/or acts of God.
A third category of heavenly beings is that of winged angels. Cherubim and seraphim make their most memorable appearances in the visions of Ezekiel (1:4-28; 10:3-22) and Isaiah (6:2-6). Cherubim function primarily as guards or attendants to the divine throne. Seraphim appear only in Isaiah’s vision and there attend God’s throne and voice praises. All three categories present us with heavenly beings in service to God. The text may focus on the service done or on the God served but rarely on the servants themselves. As a result we are left with a multitude of questions about the angelic host. Many of the most common questions asked about angels have no clear answers in Scripture. The nature of the angelic host is at best hinted at indirectly. 
Some scholars suggest that a heavenly “host” (i.e. “army”) must have order and that references to archangels (1 Thess. 4:16; Jude 9) and a special class of angels which has intimate fellowship with God such as the seraphim of Isaiah 6:2-6, indicate that angels are organized in a rigidly fixed rank system. Some authors even attempt to list their ranks and duties.
Pseudo-Dionysius, a writer before A.D. 500 who claimed to be Dionysius the Areopagite of Acts 17:34, produced a ranking of angels. His schema was later adopted by Thomas Aquinas and was not seriously challenged until the Protestant Reformation. According to Dionysius, the angels are arranged in three ranks, each rank having three groups. The highest rank (seraphim, cherubim, and “thrones”) is closest to the deity. The second rank is made up of “dominions,” “powers,” and “authorities.” The lowest rank has the most direct contact with humanity. They are “principalities,” archangels, and angels.
Dionysius’ highly speculative schema (or any like it) is flawed in several ways. Some of the entities named (“powers,” “dominions,” “principalities”) are not clearly identified in the Bible as angels at all. Others (cherubim and archangels) are never compared to one another in terms of rank. Perhaps most importantly, a schema which envisions the better angels communing with God and the lesser ones ministering to humanity has no foundation in the Bible. Scripture presents ministry as one of the most blessed of activities and God himself directly involved with humanity. Any hierarchy which serves to separate God from humanity by interposing a series of lesser beings should be suspect. 
Angels Today / Guardian Angels
In a material world that is also populated by good and evil spirits, the Bible teaches that the heavenly angels set an example of enthusiastic and resolute fulfillment of God’s will. They acknowledge Jesus as their superior, and worship him accordingly.
Angels continue to perform ministering duties among humans, and this function has led to the concept of “guardian angels, ” perhaps prompted by Christ’s words in Matthew 18:10. It is not entirely clear whether each individual has a specific angelic guardian, but there is certainly no reason for doubting that an angel might well be assigned to care for the destinies of groups of individuals such as families. These celestial ministries will be most effective when the intended recipients are receptive to the Lord’s will for their lives. 
we get to the heart of the true identity of angels in Hebrews 1:14: “Are not all angels ministering spirits sent to serve those who will inherit salvation?” This brief statement is packed with meaning.
The word “ministering” comes from a Greek word meaning “serve.” Angels are spirit-servants who render aid, and this aid is rendered to the heirs of salvation in the outworking of God’s purposes on earth.
What form does this service take? Such ministry can involve protection (Ps. 91:11), guidance (Gen. 19:17), encouragement (Judg. 6:12), deliverance (Acts 12:7), supply (Ps. 105:40), empowerment (Luke 22:43), as well as occasional rebuke (Num. 22:32) and judgment (Acts 12:23). And angelic service is rendered largely unseen and often unrecognized (2 Kings 6:17; Heb. 13:2).
Notice that Hebrews 1:14 says angels are sent to render service to the heirs of salvation. God has specifically sent and appointed angels to carry out tasks on behalf of believers; humans do not invoke or manipulate them. We must never forget that angels assist us because God has ordained it that way. There is never any sense that the sent one is more significant than (or takes the place of) the divine Sender. 
Some writers contrast the celestial beings with “fallen angels,” of which there are two varieties.
- The first consists of unimprisoned, evil beings working under Satan’s leadership, and generally regarded as demons (Luke 4:35; Luke 11:15; John 10:21).
- The second were imprisoned (2 Peter 2:4; Jude 6) spirits because they forsook their original positions in heaven. For New Testament writers they were particularly dangerous.
The precise difference in function and character is not explained in Scripture, but some have thought that the latter were the “sons of God” who cohabited with mortal women ( Gen 6:1-2 ). This view, however, is strictly conjectural. Presumably the imprisoned angels are the ones who will be judged by the saints ( 1 Cor 6:3 ). 
Angels in Renewal and Revival Movements
Leaders and followers in many of the controversial renewal and revival movements often claim to have seen or heard from angels. Given the fact that their reported messages (and sometimes actions) usually contradict the plain teachings of the Bible, it is advisable to ignore such reports.
For instance, disgraced ‘evangelist’ Todd Bentley in a 2003 article wrote:
So when I need a financial breakthrough I don’t just pray and ask God for my financial breakthrough. I go into intercession and become a partner with the angels by petitioning the Father for the angels that are assigned to getting me money: “Father, give me the angels in heaven right now that are assigned to get me money and wealth. And let those angels be released on my behalf. Let them go into the four corners of the earth and gather me money.– Cited at: Todd Bentley and His Financial Angels
There is no Biblical precedent nor any other Biblical justification for Bentley’s beliefs as expressed above. 
Some quoted entries have been reformatted for easy online reading. Some Scripture references have been rendered more completely for clarity. The text of quoted material has not been changed.
 Holman Bible Dictionary, Broadman & Holman Publishers; illustrated edition edition (April 1991). The edition quoted from is out of print, but second-hand copies may be available at the link provided. [Other Holman Bible Dictionary editions]
 M.G. Easton M.A., D.D., Illustrated Bible Dictionary, Third Edition. Thomas Nelson, 1897. Public Domain. [Easton’s Bible Dictionary for Kindle“>Easton’s Bible Dictionary for Kindle]
 Baker’s Evangelical Dictionary of Biblical Theology Baker Pub Group (May 1996). This edition is out of print but Amazon.com at times has second-hand copies available at the link provided. [Evangelical Dictionary of Theology (Baker Reference Library), 2001]
 More about Bentley’s un-biblical beliefs regarding angels
 Evaluating Today’s Angel Craze, Ron Rhodes