To intuit is to get a strong sense of something using only your intuition. You might give up on a job interview halfway through, if you intuit that the job wouldn't be a good fit for you.
When you have a hunch about something, you intuit. For example, a pregnant woman might intuit that she's having twins, and a teacher might intuit that a student is having a hard day and needs some extra attention. The earliest meaning of intuit was "to tutor," until the mid-19th century. The word comes from the Latin root intueri, "look at, comprehend, or contemplate."