First of all, you get clean reliable power, and that does affect how your amp sounds.
Second, you get a bunch of protected outlets for powering effects, a tuner, or a fan (I get really hot onstage

and you can leave all your transformers plugged in to save setup time.
Third, with a Furman you get some nice pull-out LED lights to see your amp's front panel on a dark stage...beats the hell out of the old flashlight in the mouth trick while you're tweaking knobs.
It does add some weight, but if you've got a big amp and a heavy duty case like an Anvil, it's not much in the scheme of things.
Some guys say that a $20 power strip does the same thing as a $200 power conditioner, and I don't know enough to argue with them. BUT, I worked with a sound man who was also an electrical engineer and he told me he would NEVER plug a PA or expensive amp directly into the wall or a cheap power strip.
He said a major power surge would be stopped by the conditoner, but not the strip. He also had this audio tester device that he plugged into a wall outlet and you could clearly hear a loud hiss, static, and crackling sounds. He said that was what unfiltered power sounded like.
When he plugged the device into my rack it was dead silent.
I will gladly spend $200 bucks to not worry about frying my rig.
For what it's worth...