It's a rather difficult concept to grab but, in short, the image of expansion you have in your mind is wrong. It's not your fault, it's everywhere out there, the inflatable balloon etc. And it's terrible :)
Another way to look at it is that the universe properties are changing. Whether it is infinite or finite, its size (as measured within itself) changes. Things are pulled appart. You could imagine that free vacuum keeps being generated between all objects but that would be a misrepresentation of the theory.
The most simple way I see it is actually what the equations say. It's lame but sometimes the math are the simplest way to understand a phenomenon. The equation say the metric is expanding. It means two point in the fabric of the universe are measured at increasing distances over time. As a result, unless objects are pulled to each other with sufficient force, they tend to drift appart. It's a property of the universe that has not been explained yet (at least not completely), and we still are on the fence as to what influences the expansion rate.
Ultimately, this concept is very easy to accept when you cease to represent the universe from outside of itself. The universe is everything that is so if any image in your mind represents the universe from outside, it won't give you a good picture. Balloons are especially bad :). If you need an image, draw a grid or take a notebook, draw some points here and there on it and imagine the grid keeps getting bigger and bigger. But don't look at the whole page, forget the page limits, focus on the grid. And keep in mind that the points do not expand, only the grid does...
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