A selection committee in basketball is an organization like the NCAA Men's Division I Basketball Committee, a group of 10 individuals who are responsible for selecting, seeding, and bracketing the field for March Madness.
The 10 members are made up of Division I athletic directors and conference administrators who have been nominated and chosen to reflect a fair representation of all 32 Division I basketball conferences in the US. Note that there is a separate selection committee, called the NCAA Women's Division 1 Basketball Committee, for the women's March Madness tournament.
The committee is made up of members with different areas of expertise. For example, one member will know a lot about the BIG10 and another would be a SEC expert. That being said each committee member must maintain a level of integrity, and that means not favoring the conference that they most likely had worked in.
Each member must be elected by the conference they represent, and once elected can serve up to 5 years on the committee.
The selection committee must provide an unbiased way of ranking and seeding teams in college basketball. They must choose the teams that participate in March Madness each year. Their goal is to get the best 68 teams in the country into the tournament. Half of the tournament is made easy for them, with there being 32 spots filled by teams automatically qualifying for the tournament by winning their conference. That leaves 36 spots that need to be filled by "at-large bid" teams. These are the teams that the committee must select.
The committee goes through a long process that begins even before the college basketball season does. They divvy up conferences among themselves to focus on for the season. Every member watches college basketball closely throughout the season in an attempt to get to know as many teams as possible. They reconvene sometime in February to release an in season look to how the top of the bracket would look if were released then.
The Tuesday before Selection Sunday is when things really start to pick up for the committee. From then until the bracket is released, there are countless debates, votes, and potential scenarios discussed among the members. In those five days, the committee has to finalize the bracket even though basketball is still being played in the form of conference tournaments.