As with most things in category theory, the way to really understand the Yoneda lemma is to sit down and prove it yourself. Break the statement down into the underlying definitions, draw lots of diagrams, and convince yourself that it’s true.

The other thing you can do is think about what it means for particular types of categories. For a posetal category, it says that an element of a poset is uniquely determined by the set of all elements that come before it in the ordering. For a group, it says that every element is uniquely determined by its action on the group. (This is basically Cayley’s theorem.) See this MSE post for more intuition: https://math.stackexchange.com/questions/37165/can-someone-e...