Non-violence is a funny word. People who are really into non-violence don't like it much because to say "not violent" is not quite the point. It's peaceful or friendly, kind, easy-going, harmless, things like that.
So in yoga, non-violence includes not hurting other people physically. It extends to not even thinking bad stuff about other people (or teams, as the case may be). It also means not hurting yourself in your yoga practice by overdoing it or by judging yourself negatively.
I heard someone once say that if you're conscious you won't do harmful things to yourself. If you're conscious you won't overdo things that would lead to pain, again, whether in thought or in action.
By practising the yamas and niymas (see the side bar), we become more conscious. When we're more conscious our energy is freed up and can flow and we have more presence - we're more aware and less reactive.
I'm going to practise ahimsa tomorrow when I'm watching hockey. I'm going to have my preference for a Sens win, but not be attached to the outcome. I'm going to practise ahimsa tomorrow when to go to my daughter's violin recital and sit with her father even though I can't say we're really getting along, and enjoy and celebrate her accomplishments. Ahimsa's a tricky one because it's everywhere and there are so many opportunities to practise...