Throughout many of my statistics classes, I've had my professors attempt to explain big "O" (oh) and little "o" notation (especially as it involves convergence, the central limit theorem, and the delta method). However, none of them have done a very good job at explaining this and they tend to wave their hand at it as though it's magic. Can someone please help me understand this notation? For example, in a proof (using moment generating functions) of the the convergence in distribution of independent Bernoulli($p$) variables, we are shown a step:

$[p(1+\sum_{i=0}^{\infty}{{(t/n)^i}\over{i!}}) +(1-p)]^n=[1+pt/n+o(1/n)]^n$

If you look at the RHS, you'll see this $o(1/n)$ notation. Can anyone help me understand what this means exactly?