modular arithmetic - What does "Solve $ax equiv b pmod{337}$ for $x$" mean?

I have a general question about modular equations:

Let's say I have this simple equation:

$$ax\equiv b \pmod{337}$$

I need to solve the equation.

What does "solve the equation" mean? There are an infinite number of $x$'s that will be correct.

Does $x$ need to be integer?

Thanks very much in advance,

Yaron.