My goal will be to motivate why looking at distribution algebras associated to p-adic lie groups is natural in the context of number theory. More specifically I will try to briefly outline their importance in the p-adic Langlands program. And then I will give a simple example of an overconvergent distribution algebra of certain kinds of  p-adic groups with an eye towards illuminating techniques used in my work Dagger groups and p-adic distribution algebras (joint w/ Matthias Strauch and Claus Sorensen).