When a student athlete verbally commits to attend a particular school before signing a contract, there is a verbal commitment. It sends a signal to other college coaches that this athlete no longer needs to be recruited by them because he has already made up his mind. It also can simplify the recruiting process.
However, a verbal commitment does not mean that it is already a binding agreement. It is not a guarantee of a scholarship. Verbal commitments are not recognized by the NCAA. There may also be the scenario that a university withdraws its offer on short notice. Therefore, it is important for a student athlete to still maintain a good relationship with all other colleges.
Since there is currently no rule from the NCAA as to when an athlete can commit to a college, it is always possible once the college coach has made an offer to the student.