Practice?

The word practice as applied to professions has always puzzled me. Personally I don't want to go to someone about a medical problem,or even a legal problem if they are only practicing,I want them to know how! It just seems like a backward phrase for those particular professions considering all the years of schooling they go through before they can begin their practice. Before I sat down here today to write this I was going to try to get to the bottom of why it is referred to as practicing but found out after nearly an hour of trying that I wasn't any closer to an answer than I was when I started. The two dictionary terms I found that applied are as follows,but once again shed no light on the real question at hand.
Practice
1. to do repeated exercises for proficiency
2. to pursue a profession actively
Is it just me,or does this seem to leave out something?