The theorem is fundamental to the deeper understanding of Boolean algebra that emerged in the first half of the 20th century.
[1] Stone was led to it by his study of the spectral theory of operators on a Hilbert space.
The points in S(B) are the ultrafilters on B, or equivalently the homomorphisms from B to the two-element Boolean algebra.
This is the topology of pointwise convergence of nets of homomorphisms into the two-element Boolean algebra.
Conversely, given any topological space X, the collection of subsets of X that are clopen is a Boolean algebra.
An extension of the classical Stone duality to the category of Boolean spaces (that is, zero-dimensional locally compact Hausdorff spaces) and continuous maps (respectively, perfect maps) was obtained by G. D. Dimov (respectively, by H. P.