in your example, 18x9 et +25
18 in the diameter, and 9 is the width as you say.
the width is messured from the inside of the wheel, where the bead of the tyre sits on each side.
offset is the amount in mm that the mounting face of the back of the wheel is offset from the centre of the wheel.
so on a 9" wheel, offset zero would mean the back of the hub is exactly 4.5" from both edges of the wheel.
a positive offset is where the hub is towards the front of the wheel pushing the barrel in to the arch (less dish)
negative is where the hub is towards the back of the wheel pushing the barrel out of the arch (more dish)
low offset or better yet, negative offset is best for deep dish wheels for serious stance.
and just to ad, adding spacers lowers the offset by whatever thickness the spacer is.