Technically speaking, SESAC stands for the Society of European Stage Authors and Composers, though today the company is known exclusively as SESAC. The company was founded to provide European songwriters with a US presence - hence the name - but the company has changed dramatically since then. SESAC now has a global reach and as such has distanced itself from its original name.
SESAC is a performance rights organization (aka, performance rights group, performance rights society). They collect and distribute royalties for public performances of the music of their clients. SESAC is unique among US performance rights organizations in that they are actively selective in choosing their clients rather than simply accepting everyone who applies.
Learn more about performance rights organizations: