Fred Maia W5YI used to explain this about every other month in his column in CQ Magazine.
There are basically four groups of callsigns issued to U.S. amateur radio operators and the groups are based on rules set up by the FCC. There are some exceptions to these rules (notably the geographic restrictions for Alaska, Hawaii, Puerto Rico, and U.S. possessions in the Caribbean and Pacific), but these are the basics:
Group A consists of 1x2, 2x1, and 2x2 callsigns. Group A callsigns are only issued to Extra class licensees. A 1x2 call sign can begin with K, N, or W. A 2x1 callsign can begin with AA through AL, KA through KZ, NA through NZ, or WA through WZ. A 2x2 callsign in Group A begins with AA through AL.
Group B consists of 2x2 callsigns and are only issued to Advanced class licensees (while no new Advanced licenses are being issued, there are still over 59,000 valid Advanced class licenses in the database). A 2x2 callsign in Group B can begin with KA through KZ, NA through NZ, or WA through WZ.
Group C consists of 1x3 callsigns and are only issued to General and Technician class licensees. A 1x3 callsign in Group C can begin with K, N, or W.
Group D consists of 2x3 callsigns and they were being issued to Novice class licensees when the Novice test was still being given (there are still 16,000 Novice licenses in the database). A 2x3 callsign in Group D can begin with KA through KZ, NA through NZ, or WA through WZ.
You can hold any license from the group you are eligible for by license class or from a lower group (subject to geographic restrictions). If there are no licenses available in the sequential callsign system in the group you are eligible for, the FCC moves down to the next group.
For example, there are no more sequential Group C callsigns in call districts 0 through 9. If you pass the Technician test, you are eligible for a Group C callsign. Since none are available in the sequential callsign system, the FCC will issue you the next available Group D callsign.
The vanity callsign system allows you to request any available callsign rather than take the next available callsign in the sequential system, but you may still only hold a callsign from the group you are eligible for. If you hold a General license, you can request any available Group C or Group D callsign subject to the rules for vanity callsigns.
To answer the OPs question, there is a check box on the Form 605 that you fill out when you take your next test. That check box indicates that you want the FCC to issue you the next available callsign in the sequential system in the group you are eligible for. If you hold a Technician license and pass the General test, you are still only eligible for a Group C callsign. If you don't want to change your callsign, don't check that box on the 605.
To see the next available callsigns by Group and by district, go to:
AE7Q's Amateur Radio Database Query Tools