In an online problem, you are required to make decisions without knowing all the inputs.
In most computer problems, you are given all the inputs at the beginning. We call those offline problems.
Life is an online problem. For example, you must make decisions today without knowledge of what tomorrow will bring.
Algorithms are, by definition, deterministic. This means that, given certain inputs, the algorithm will make a predictable choice. A randomized algorithm, on the other hand, given certain inputs, will make a given choice with a predictable probability.
I will give an introduction to this fascinating new area.