what does a power conditioner really do?

As many others have emphasized, the quality of power into your home is important. I'd say equally (if not more so) important are the other devices in your house. Many audio components have some aspects of what a power conditioner does, built right into them. Other devices in your home can create significant electrical noise (think major appliances).

A power conditioner may offer the following features:
- Surge protection (MOV, avalanche, etc...)
- Power regeneration (very inefficient btw, if you care about your electrical bill)
- AVR (automatic voltage regulation)
- Voltage monitoring (may shut off power if voltage is too high/low)
- Isolation transformer (like in RGPC products, or an APC H15)
- RFI/EMI filtering, often with CMC's (common mode chokes)
- May provide balanced power (BPT, Equi=Tech)

I'm sure there's more, but I think that covers most power conditioners. I haven't seen much data about how effective they are in real world environments, or even controlled blind tests to show audible improvements. It's easy to create conditions to verify that the conditioner does what it advertises (i.e. feed it 100V, and it boosts it to 120V, or verify the surge protection meets the advertised specs), but knowing whether these conditions occur in your home or would even have any real noticeable effect on your equipment is a totally different story (and hard for anyone to say, because different people have such different equipment).

If you don't have a very power hungry system I found that PS Audio's P3 or P5 work rather well.  My system has more bloom, bigger soundstage, darker background.  They aren't cheap though.  

Shunyata hydra and power cords really dropped my noise floor.    I didn't really wanna think it would but once demo in my house it was an eye opener.   I'm in a loft building with 15 amp service running tube and ss gear .     I think conditioners are not gonna make a mediocre system great but they will make a great system just a touch more accurate.     Prior to the shunyata I had just a monster power strip plugged into a Panamax.     That combo did not seem to do nearly as much on my setup .   

Over a number of years I have acquired several PS Audio "PowerPlant" models — all either "B stock" or at discount. I have opened these up and found them to be well constructed with high quality components. They work great at cleaning up power and providing protection against power line borne transients. They also buffer power for peak demand.

I have demonstrated their benefits to friends, and all can easily hear the difference in terms of both a non-existant noise floor and increased dynamics. They really shine with prolonged dynamic music when played at higher volume. You will get these benefits with or without upgraded power cables, but those will also contribute additional benefit. 

By upgrading your power to clean and "buffered" power and using EMI/RFI shunning interconnects, you will hear a difference. To me that is the motivation for the spend, but the protection factor is as important.

     As well as providing (Often) sequential turn on or your components, a power condition, a power conditioner tries to make up for amplifier and preamp designs that do not have a well designed power supply, IMHO.
     They also give the retailer something else to sell you.
I prefer my 10 gauge, 30 amp wiring and electronics stuffed with big transformers and lots of big filter caps.
     I tried Classe, but I believe their gobs of small caps do not focus as well as the big ones in other brands. 
     Of course, other associated parts could be the difference.
     I am comparing Classe to things in the same price range and below.