For almost finite groupoids, we study how their homology groups reflect
dynamical properties of their topological full groups. It is shown that two
clopen subsets of the unit space has the same class in H_0 if and only if there
exists an element in the topological full group which maps one to the other. It
is also shown that a natural homomorphism, called the index map, from the
topological full group to H_1 is surjective and any element of the kernel can
be written as a product of four elements of finite order. In particular, the
index map induces a homomorphism from H_1 to K_1 of the groupoid C^*-algebra.
Explicit computations of homology groups of AF groupoids and etale groupoids
arising from subshifts of finite type are also given.