It depends on how your AVR/low pass filter is configured and subwoofer is connected; typically you will configure a cutoff at a point the speakers are starting to struggle to allow the speakers to focus on doing what they do well; this also allows more power to the speakers to be focused on the middle and treble range potentially enhancing them as they're not sinking power into the bass frequencies; whilst the Subwoofer does the heavy lifting. It does depend on how you've got it configured though, it is also essentially possible to run the Subwoofer off the same output as the speakers; in which case the subwoofer and the speakers can essentially be trying to transmit those bass frequencies. Typically this doesn't sound as good though as the Subwoofer bass and speaker bass will not always be in sync, and the speakers will likely struggle much more easily with lower bass frequencies.
Typically the best way to think of a subwoofer in a proper AVR setup is that, with the Subwoofer off, your sound will still sound normal, just lacking 'weight' with the subwoofer off, when you turn the subwoofer on, the sound range will 'fill out'; and the bottom will come alive.
Typically your subwoofer cut (dependent on your speakers) is somewhere around the 60-100Hz region, so with the Subwoofer off, you will still have all your mid bass, mids and treble, you just won't have the very bottom end. It not only adds extra punch; it can often go considerably lower; and considerably cleaner (AKA proper bass rumble you can feel, and not just fart/distortion you hear)
At one point during moving out I had to get rid of the nice subwoofer I had at the time; NOTHING felt quite right without it after having got used to one; I wasn't able to get anything anywhere nearly as nice; but I put a subwoofer back into the setup in my new place as soon as the wife would allow me to; it added immensely for games and movies, and was beneficial for a lot of music too.
A good subwoofer will allow you to hear and feel things a cheap subwoofer or most speakers just cannot.
If your budget isn't too high, check out BK Subwoofers; they are typically VERY good for the price compared to larger brands; partially because they mostly build for other firms, and thier own designs they sell direct.
Example review:
BK P12-300SB-PR Subwoofer Review | AVForums