I was reading about this today. For those unfamiliar with this big word, a simple explanation is the process of being made holy. There are people who believe there are two steps to knowing Christ. One is salvation, the point where we surrender to God, ask His forgiveness and are made clean.
Now some people believe that sanctification happens right then and there. From now on you are perfect. Some people even believe that they do not sin after that initial point of sanctification. Any "sin" that happens happens because of a fallen world, not their choices.
Others believe that sanctification occurs later. That at some point later in your walk with Jesus you are made holy. You are again made perfect, just not at the point of salvation, and you again cannot sin, but this happens much later and some people never reach it.
The other view is that after salvation people are constantly in the process of sanctification. You will never be completely holy, but you will be striving for it. You will be doing what you can to live for God and in that way be continually sanctified.
It's funny, in reading Romans 6 I can see where all three of those views come from. But I think the key is your choices. The key is living like you are either sanctified or are in the process of being sanctified. I don't know which one is 100% right, but I know they both say that we should act in a way that we are holy. Romans 6:13 says "Do not offer the parts of your body to serve sin." (NCV). We should be making the choice to not sin, the choice to live as holy as we can.
It's interesting to think about. Personally, I would love to say I'm perfect and holy, but I don't think I'm there yet... :)