Binding and Loosing
Matthew 16:19, "And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven."
Jesus referred to binding and loosing as the keys to the kingdom, which means we ought know and use these keys, don't you think?
Binding
Binding is like a temporary spiritual handcuffing. You can bind a demon spirit, much like tying something up with rope or chains. You cannot bind a person's free will, but you can bind the demons affecting or influencing that person. Binding is NOT the same practice as casting out demons, casting out demons brings fourth lasting results, whereas binding is only to tie them down for a period of time. If you are trying to talk to or minister to somebody, and they seem impossible to get through to it can be helpful to bind up the spirits inside that person, which will handcuff the enemy so you can directly and effectively minister to that person without having them continually held back by the enemy's interference. Another good time to bind is when the person isn't ready for a deliverance and you are not willing to put up with their demonic personality. I have a friend who bound demon spirits which were in her teacher, who was a lesbian, and she stopped giving her any troubles since then! Was the teacher ready to be delivered? Highly unlikely. But that doesn't mean you must live with her demonic personality, simply bind it whenever you are around that person, and it handcuffs the enemy from doing his work around you. Another good time to bind, is when you are half way into a deliverance (let's say you got 20 out of 40 demons out) and you need your rest, like say it's 2am and you have to work the next day. You could simply bind the demons overnight, and finish the deliverance the next day.
What does it mean to bind on earth? It refers to your physical location; right now, you are here on earth. Jesus is saying that the authority to bind and loose are provided for us to use right here on earth.
What does it mean for something to be bound in heaven? If you look up the word 'heaven' in the Greek, you'll find another word called 'air', which is where the spirits dwell. The Bible also says that we are seated with Christ in heavenly places. This isn't referring to heaven as in the place we go after we die, but rather a realm. The Bible tells us that we are seated in the heavenly realm with Christ (Ephesians 2:6). We, as humans, were below the angels and demons, but as believers, we are now seated above the angelic realm and seated with Christ! So the word 'heaven' here is referring to the spiritual realm, the air, where the spirits dwell and operate. In Ephesians 2:2, Satan is known as the 'prince of the power of the air'.
Therefore, when you bind something here on earth, it will be bound in the spiritual realm as well. This gives us the ability to bind demons, because they dwell within the spiritual realm.
Binding is a powerful witnessing tool: What keeps a person from accepting Jesus? The god of this world, which is Satan (working through his army of demons) has blinded their minds from the light of the gospel (2 Corinthians 4:4). Jesus taught us to bind the strong man, then we can plunder his house (Mark 3:27). If you have been trying to witness to somebody, and seem to be getting nowhere, try binding the spirits of darkness that are preventing that person from seeing the light in the gospel. You cannot bind a person's will or force them to accept the gospel, but you can do something about the demons which are holding the person back. Once you take the demons out of the picture, you will be able to talk directly to that person without demons whispering in their ears and trying to combat what you are telling them.
Loosing
Loosing, like binding, can be done here on earth, and takes effect in the spiritual realm. Loosing however, refers to the loosing of a captive or person in bondage. You bind demons, and you loose the captives. When Jesus set free the woman with the issue of blood, He said unto her, "Woman, thou art loosed from thine infirmity." (Luke 13:12)
Other common theology on loosing: Many people believe that loosing refers to the act of loosing good things into a person's life, such as blessings or God's love. My opinion is that God's love is not bound in the first place, therefore there is no reason to loose it. I have never seen any Biblical backing for the concept of loosing good things into a person's life. But if you look at Luke 13:12, it gives us an example of when Jesus loosed a captive, "And when Jesus saw her, he called her to him, and said unto her, Woman, thou art loosed from thine infirmity."