[S]ome Christians accept the notion of ‘territorial spirits’ as readily as pagans, the only difference being that they believe that such ‘spirits’ should be confronted through authoritative prayer and commands issued ‘in the Spirit’.
– Source: Territorial Spirits, by Charles Hoole, Evangelicals Now, Mar. 1998
The concept’s main proponent is C. Peter Wagner, who has influenced countless Christians — mainly within Evangelical, Charismatic and Pentecostal traditions — to wage spiritual warfare against what they view as ‘spiritual strongholds.’
Many Christians have also been influenced by descriptions of angels, demons, and spiritual warfare in the fictional books of Frank E. Peretti.
Simplified examples of the battle against territorial spirits may include believers praying against the ‘Spirit of Lust’ over Amsterdam’s Red Light District, against a ‘Spirit of Greed’ over portions of Las Vegas, or ‘Spirits of Witchcraft’ over sections of New Orleans.
The problem that comes with the use of the term territorial spirits is that some Christians believe it is their duty to engage territorial demons in spiritual warfare. This, however, simply cannot be justified by Scripture. There is not one instance in the Bible where someone actively sought out a demon in order to engage it. Demon-possessed individuals were encountered, and even brought to Jesus and His disciples for healing, but the disciples didn’t go out looking for demons to cast out of people. Nobody in the Bible ever prayed that the demon princes of their town be bound from working their will against the residents of that town.
Territorial spirits, whereas not being a Scriptural term, may very well be appropriate as exampled by the aforementioned passages. Such a term is really not that important, though. What is important is our response to that term. A believer in Christ does not have any biblical support in offensively engaging in prayer-led spiritual warfare against demons. Rather, a believer needs to be aware that there is a spiritual battle, and to take it seriously. Our lives need to be focused on prayer, and on growing in faith. Should we ever encounter a demon, we definitely have the Christ-given authority to deal with it, but we should not go looking for them, territorial or otherwise.
– Source: What are territorial spirits?, GotQuestions.org