Try to search YouTube or elsewhere for an example of a downsampling/bitcrushing pedal. Anything that can reduce the sample rate. If you turn the sample rate way up, you hear your unaffected signal. But as you start to reduce the sample rate, you start to hear odd atonal distortion products. That's aliasing. Basically the sample rate becomes lower than the highest frequency of your signal, but those frequencies are still coming in, so the electronics has to do something with them (it's not smart enough to just discard them), so what ends up happening is the higher signal is "read" at random points along its waveform, and a new wave is constructed from those data points which is lower in frequency and harmonically unrelated to the input signal.
For more info on aliasing, look up Nyquist and stuff about sample rates.
Now that's out of the way, I can say with reasonable certainty that when most people say "so much digital aliasing sound on multifx" they have no idea what they're talking about. Digital multi-effect pedals may not have cutting edge sample rates and A-D/D-A converters, but generally they are fast enough to not cause aliasing (at least not audible aliasing). However, they may have latency and phase issues that do come across as audible "weirdness." That sort of problem will make it sound fine once its recorded, but playing it in real time will sound artificial and have a weird feel. That's probably what most people are really talking about when they say things like that.
