"If they have escaped the corruption of the world by knowing our Lord and Savior Jesus Christ and are again entangled in it and overcome, they are worse off at the end than they were at the beginning." NIV translation
If they have the knowledge of Jesus Christ in their heads which can drive out the evil but their heart is not also filled with the Spirit, they are worse off than if they had never heard the good news. Without the Spirit, they can easily be deceived by the false teachers that Peter is speaking about. This is what Jesus was talking about (in Luke 11:24 - 26) when He spoke of the evil spirit returning to the empty house with seven of his friends. There are many, today, that fall into this category as they have been taught that Jesus loves them but they have never been taught what that means. The Holy Spirit is the One that can guard our hearts and so our "house" is not empty and cannot be occupied again by the evil of this world.
"It would have been better for them not to have known the way of righteousness, than to have known it and then to turn their backs on the sacred command that was passed on to them." NIV translation
Many have used this verse to promote the idea that we can lose our salvation but that is not what Peter is saying. What he is saying is that it would have been better for them not to have known about the Way (Jesus) than to have known (mentally) but not had a change of heart and really known Him.
We can know of Jesus without personally knowing Jesus but personally knowing Jesus is the only way that we can have salvation.
"Of them the proverbs are true: 'A dog returns to its vomit,' and, 'A sow that is washed goes back to her wallowing in the mud.'" NIV translation
Even though it may be disgusting, anyone who has had a dog for a pet will tell you that they do return to their vomit. Peter quotes part of Proverbs 26:11 here to make the point that, those that have turned their back on the ways of God, are just doing what they do because of their nature. Many have used this verse to say that it is talking about losing your salvation but that is not so. When we come to Jesus, we are a new creation and so we have a new nature. We go from being that dog or sow to being a part of the royal family of God.