Liberty is different than Leave.  Leave is similiar to requesting time off for vacation at work, they must submit a chit and have it approved.  Liberty basically means that they have "liberty" to leave the base but they are still "on duty" and cannot travel far and they are still accountable for their whereabouts and some even have duty while on liberty.

There are three (3) phases of Liberty - all of which must be earned.  They can also be taken away!

Phases are like being a freshman, sophomore, junior, senior. They get different privileges depending on how long they have been at school. Phases are the same at "most" A schools, but the amount of time in each phase varies between schools and can vary between rates (a rate is the term for the job they will hold).

Phase I is for sailors who have just arrived. They are required to wear their uniforms at all times outside of their barracks, are not allowed to leave base and are required to muster three times each day. 

Phase II sailors have been at the school for an average of 2-6 weeks. They can wear civilian clothes and they can go off-base - only with a liberty buddy.  They are not allowed to stay out overnight.

Phase III are sailors who have been at the school approximately 4-12 weeks and have shown personal responsibility. They no longer have to attend evening muster and can stay out overnight.

Student sailors may be "phased back" or denied the next phase if they fail inspections, miss PT or morning muster or otherwise get in trouble.  Even while in Phase III, there are certain cities they are not allowed to go to and there is a mileage boundary line which is unique for each A-School.  For example, NASP/Corry Station in Pensacola, FL do not allow sailors to go to New Orleans.