S.T.B. (Sacrae Theologiae Baccalaureus) refers to the academic degree Bachelor of Sacred Theology.
The Bachelor of Sacred Theology is offered by a number of theological colleges. It is sometimes offered as a graduate degree, for students who have already completed a BA or other first degree. It can also be offered as an "ecclesiastical degree", granted directly by church hierarchy after one has completed requirements in addition to those necessary for a civil degree, but which are required for ordination.
Within the Catholic Church, the STB is the first of three ecclesiastical degrees in theology (the second and third are the Licentiate of Sacred Theology and Doctor of Sacred Theology respectively), and as such is granted by pontifical faculties under the authority of the Holy See. It is awarded upon successful completion of the first cycle, a three-year course of studies that aims for a comprehensive competence in theology.
Despite its name, the STB is a graduate degree, at least in the US. While acceptance to an STB programme always requires at least two prior years' undergraduate study of philosophy, as well as knowledge of Latin and Greek, in the United States a completed undergraduate degree is generally required for admission to an STB programme. Thus it is roughly equivalent academically to an MDiv (although the STB has a more academic focus while the MDiv has a more pastoral focus), and the two are sometimes granted together.