For a differential equation like dy/dx = f(x,y), it means that the solution which passes through the point, say (a,b), will have slope f(a,b).
That means we can attach a slope to each point in the x-y plane ... so long as f(x,y) has a value at that point.
That means ...

>Can you get to the point?
Okay. Here's a spreadsheet where you type in f(x,y) and you get a bunch of those slopes:

>And it plots a particular solution?
Yes, by "numerical integration" of the differential equation ... using Runge-Kutta.
It's fun. Try it!