I agree with lalalalisaaa, but furthermore, he is also describing that every heart has the capability to heal itself and open itself up to the chance of love again. It is also very much pointed toward one person in his life (at the time he wrote it, I don't know who that would have been), and he's saying that at first he was walking on egg-shells with her, not wanting to upset her or ruin the chance before it even started, then he says that he has pushed her away (when he talks about his silence), which can probably be contributed to the fact that there were some mixed signals between them. Then of course, in the end he gives in and confesses that he wants to be with her and he throws himself (his heart) out there for her to decide if he's worth taking the chance on.

He's saying that he is going to miss all the times he's had where he was footloose and fancy free, and now he has to buckle down (again) and go to work, and put away all of the finer things in life that he has been used to. This is of course (in real life for him) the result of his bankruptcy which was caused by his finance manager (who was embezzling money from Mr. Joel, and just plain overall being a jackass with Billy's money). But, like the classic and unshakable Billy Joel we all know, he turned it around and he did go back to work even turning his bankruptcy and divorce into songs that we all know and love. Go Billy.