accept_rate is the internally tracked value of the user's Accept Rate. This is roughly a measure of how many of the user's questions have answers and where one of the answers was accepted by the user.
For the actual details of how it's calculated, read the blog post announcing accept rate. In a nutshell:
- The user must have 4 or more questions.
- Only questions older than 3 days are counted.
- The question must have at least one answer to be counted. Answer score does not matter.
- Closed questions and Community Wiki questions do not count.
Also note that "the community" decided not to publicly display the accept rate as of January, 2013.