“Territorial spirits” is a term some Christians use to identify demonic occupation of a specific geographic location. Ironically, it is also a term pagans use to describe an otherworldly presence believed to be residing in a specific geographical location.
The Christian concept of territorial spirits comes from passages such as Daniel 10; John 12:31; John 14:30; John 16:11; Mark 5:10; and Ephesians 6:12. All of these passages imply that fallen angels have been given some type of responsibility over a certain area. Thus, they seem to be territorial. However, we need to remember that this teaching is inferred; the Bible never explicitly delineates a hierarchy of demonic authority in the world. What the Bible is clear about is that demons are at work in the world and that believers are very much involved in a battle against them.
In Daniel 10, for example, an angel struggled against a demonic adversary the entire time Daniel was praying and fasting. It wasn't until the end of Daniel's spiritually focused time that the angel finally broke away and came to Daniel. Ephesians 6 exhorts believers to stand firm against our spiritual adversaries and to remain alert and ready for battle. There is no doubt that our struggle on Earth is mirrored in some way in the spiritual realm.
The problem inherent in the term “territorial spirits” is that some Christians believe it is their duty to engage territorial demons in spiritual warfare. This, however, cannot be justified by Scripture. There is not a single instance in the Bible where someone actively sought out a demon in order to engage it. Demon-possessed individuals were encountered, and some were brought to Jesus and His disciples for healing, but the disciples didn't go looking for demons to cast out of people. No one in the Bible ever prayed that the “demon princes” of a town be “bound” from working their will against the residents of that town.
Territorial spirits, although not explicitly a scriptural idea, may very well exist, as seen in the previous passages. Whether or not a spirit is “territorial” is really not that important, though. What is important is our response. A believer in Christ has no biblical support to engage 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 (1 Peter 5:8). 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.