I went to a Skrillex concert last year. When Skrillex performs live, what is he doing?
Electronic music live acts are normally performed using sequencers that trigger synthesizers and/or samplers, plus an array of controls like knobs and faders. It's common for the sequencers to control the rhythm and pitch, and the knobs and faders to control volume and timbre, but you can make the sequencers and knobs/faders control something else inside the limits of the device.
From this video we can see that Skrillex is using Ableton Live as a sequencer, but it is more accurately defined as a non-linear DAW (you can think of it as a very powerful hybrid of sampler, synth, mixer, and drum machine).
He is also using a M-Audio Trigger Finger as a control surface, which includes faders, knobs, and pads to control whatever you program them to control in Ableton Live. Maybe he bought this bundle:
This type of setup (Ableton Live + a control surface) is the most common setup for electronic music live performance now days. When using analog synths, a common setup is to use Live as a sequencer (using MIDI tracks) that feed analog synths (you can see James Holden doing it here, Surgeon doing it here, both using modular synths).
In general, that's what he is doing (ideally, more on that later). Using a control surface to control Ableton Live (if he is doing anything at all, electronic music has its own "lip-sync" issues). Inside Ableton Live you'll find synths, samplers, audio tracks, effects, and whatever audio processing and production dynamic you can think of.
What synths, effects, etc is he using? The video suggests that Skrillex is using one knob to control a stutter effect (Live's beat repeat effect, most likely), but it's hard to know for sure.
Because of some interviews (and this page, specifically) we know that he uses stuff like Massive (very common in Dubstep production), Sylenth1, and Reaktor. Through the Finger Trigger he probably controls things like envelopes, LFOs, delay times, distortion amount, etc.
With that said, without having the actual Ableton Live patch it is hard to be specific about what he is doing. The control surface might not even be connected and everything is already automated and/or pre-recorded. Or maybe he has intimate control of every single dynamic.