Sidechain literally means an effect that has a "side" input so that you can feed a signal in to modulate the effect.
Usually when people refer to side chain they are refering to sidechain compression.
In this instance it would be used on a bassline and with a the feed of a drum beat into the sidechain so that when it "kicked" it would activate the compression, effectively lowering the signal of the bassline.
This is used alot for "ducking" so that you dont have your kick drum and you bassline at full volume at the same time, clearing up the lower frequencies in use by the bassline and kick at once, so that the kick have more "space" and sounds more defined.
When used with more aggressive settings the effect of this is a "pumping" sound used alot in electro and french house etc, where the bassline seems to surge in on the offbeat. You can achieve different kinds of feels with different attack, release, ratio etc. settings.
You can also achieve some really cool effects by using a sidechain on other things, like hi-hats and it works especially well on pads.
You dont have to use a sidechain source that is audible, in other words you dont have to route the sidechain source into your mix, if you dont then you can do some cool sidechain patterns that arent based around how you have your rhythm arranged.
Logic has a badboy and simple to use sidechain compressor and Live 7 has a sidechain on its compressor (about time) but I havent managed to get me a beta key yet so cant comment on how well it works or how easy it is to use.
Have a search around, theres LOTs of info around the net and also on this forum about sidechaining.
As for how to make the kind of bassline that Erik Prydz uses, he likely is using outboard analogue gear, but you can get those big phat basslines out of nearly any soft synth. its not so much in the synth but knowing how to engineer the sound you want, layering oscillators with the right waveforms in the right amounts etc.
Obviously you will get different results with different soft synths, as you do with different hardware synths doing the same thing, but understanding how the synth works is more important than trying to find a magic VST to make the sound you want. You are best learning one VST really well and then you will learn largely how they all work and be able to appreciate the differences between them.
I have started using Operator almost exclusively since buying it as Ive found I can get just about any sound I want out of it. The one other VST I use for basslines is called Chips32, its free and its a very simple wavetable synth. You can get some VERY phat square wave basslines out of that with minimal tweaking, some compression and reverb.
Hope some of my drivel has been of interest