It’s all too easy to assume that someone else will nominate a worthy colleague. But someone has to do it, so why not give it a go? It can be an enjoyable experience to prepare a case and explain why someone is worthy of recognition. In my experience you usually find out something you did not know about the candidate’s work or the field. And of course if you harbor ambitions to be nominated it’s only reasonable that you act as nominator yourself from time to time.
You should first check that you are eligible to nominate. For some of the big international prizes you have to be invited to make a nomination. But for math society prizes it is usually the case that anyone can make a nomination (and self-nominations are usually allowed, though are uncommon).