It helps to be familiar with basic functions commonly found in math (and physics, for that matter): sine, cosine, exponential, polynomial, reciprocal, etc. You can form a mental picture if you have already seen a particular class of function many times before.
If a function is some complicated mixture of other functions, one may just have to create an actual graph rather than trying to visualize it mentally.
What an equation "describes" depends upon the application, not the equation. Exactly the same equation may describe many different situations. If you mean "given an equation, determine some some situation that it might describe", perhaps to give you some ideas on how to simplify the equation or do something else with it, that comes with having done lots and lots of appliations.