Why do we say that someone “practices” law or medicine?

The word’s earliest meaning was, in the OED's definition, ‘to pursue or be engaged in (a particular occupation, profession, skill, or art)’. It is first recorded as such in 1421 and that is the meaning it continues to have when we speak of practising (BrEng spelling) law or medicine. At around the same time, it seems to have been used to mean ‘to exercise oneself in a skill or art in order to acquire or maintain proficiency, especially in music’, but it is not until 1542 that it is recorded as meaning ‘to perform (an activity) or exercise (a skill) repeatedly or regularly in order to acquire, improve or maintain proficiency’. That is the meaning it most commonly has today.

One of the principle meanings of practice is

the continuous exercise of a profession b : a professional business; especially : one constituting an incorporeal property

This derives no doubt from earlier meanings of systematic performance of a skill or action.

The term is not limited to law and medicine. Consultancies, engineering firms, architects, and many other kinds of professionals also refer to their firms, specialties or lines of business as practices.