Libint is two things:
1. a library of C/C++ functions for efficient evaluation of
several kinds of two-body molecular integrals over Gaussian
functions;
2. the optimizing compiler that generates a Libint library.
In molecular electronic structure theory Gaussian basis sets are
standard because they allow efficient evaluation of matrix
elements of operators (molecular integrals). Modern electronic
structure programs spend considerable portion of their runtime
computing the Coulomb two-electron integrals. While anyone can
compute Gaussian integrals using simple formulas, the efficient
evaluation of many-body can be (relatively) complicated.
Libint is an open library that anyone can use to compute a
variety of two-electron integrals, most importantly the Coulomb
two-electron integrals and their arbitrary-order geometric
derivatives, over Gaussians of arbitrary angular momentum.
Among other notable features is the support for the nonstandard
two-electron integrals that appear in explicitly correlated R12
methods.