Paul, there are two stages of amplification that take place, regardless of whether a receiver or a separate pre-amplifier plus amplifier are being used. The pre-amplifier first increases the voltage coming in from the player or other source component about 4-5 times; the amplifier then increases this voltage about 25-30 times more, so the net result is an increase of about 100-150 times, which is enough voltage to drive speakers to very loud levels.
The pre-amplifier section of the receiver or separate unit also controls the various functions which other replies have listed. The volume, for example, is controlled by a variable resistor which varies the amount of the incoming voltage which is subject to the fixed 100 or so times "gain" mentioned above from almost 100% to almost none.
A separate amplifier can't improve the sound unless what you have is inadequate for the volume levels needed. Your 3311 is rated at 125 watts per channel, and this is the one area of audio that can be relied on as accurate, since it's subject to legal regulations of the FTC. Your 3311 can drive your speakers to beyond safe(to your hearing)listening levels, and more isn't needed. As Kruncher quoted me above, unused headroom is simply that: unused.
Your equipment, with one exception, is excellent, and it's agreed that a quality sub is what will improve your listening experience.
With all respect to JohnK I have to go against the prevailing wisdom here and say that a new amp would likely make the biggest improvement in your listening experience. I'll explain why but it's a bit of a long story...
First of all, I was until recently in a very similar (and happy!) situation to Paul. I have a Denon AVR4802, which is a ten year old receiver also rated at 125Wpc -- a bit older than Paul's but also somewhat higher in the Denon food chain in its day. My front speakers are a pair of M80v3's and a VP180. I had no amp and it was good! The Axioms are truly a fine set of speakers!
Then I heard on the forum about the newly released LFR1100's. I had to jump on the pre-order pricing and am now the owner of a set, although I've not finished setting them up. Of course, part of the reason for that is that I now need four channels of amplification for the LFR's. I was in the process of acquiring some good Bryston amps on the used market when, wouldn't you know it, Axiom announced the new ADA amps. Of course I jumped on the pre-order pricing for that and have recently received a new four channel ADA 1500 with the idea that, if I didn't like it for driving my main speakers, I could use it for the rear channels of my HT when I eventually get a new room built in my basement and spring for a set of QS8's.
Anyway, I of course became curious: how much of a difference would the amp alone make in my existing system? I, like some of the others on this forum, didn't think there would be much difference, if any. But why not give it a try as I build up my system in preparation for the LFR's?
So I did. I took the front L & R pre outs from my 4802 and connected them to two of the inputs on the ADA1500. Then I disconnected the speaker outs from the receiver and re-connected them to the outputs of the ADA1500. Then I gave a quick listen... which became a long listen... and WOW!
There was an immediate and obvious improvement in sound, both for stereo music (from CDs) and surround sound music (the Peter Gabriel Secret World concert DVD). This improvement included much tighter, punchier bass, improved clarity, and more pronounced highs. Actually the bass was so much better I had to check if I'd accidentally changed a setting on my subwoofer but the improvement was still obvious even with my sub turned off. (It didn't seem to add too much, which I guess makes sense given that the M80's and VP180 can go quite low on their own. Note that I'd already set the 3 front channels as "large" in the receiver setup and that did make a big difference compared to "small".)
I'm quite honestly amazed at how big a difference just adding two channels of ADA1500 power to my existing system made!
I hope this posting helps.