I guess I haven't used "on your left" while biking, nor had it used on me. We're sparsely populated, and I don't encounter a lot of riders on my road rides. I guess it hasn't occurred to me to say it - I generally cough or something, so they know I'm there. I use it a lot in ski races. In striding races, it's always (well, at least the last 30 years that I know of) been a rule that the slower skier in the tracks relinquish them to the faster skier coming up behind. Proper etiquette is to yell "Track! On your left!" Or right, as the case may be. Skate-skiing, in a race, you yell out the side to plan to pass on, and they are supposed to get over the other way (or pull their equipment in enough to allow the pass). I do encounter people who either speed up or refuse to get over, but that is against the rules, and they really should be disqualified for it. The main thing is to select an area where it is actually possible, and not going to send the person into the bushes, a rock, etc. To be polite. I try to select the inside of a curve where I can get past as quickly as possible, although I had one woman gripe about that (because I was making her take the longer route - however she'd been preventing me from passing for a while, so I didn't really have a choice - I could have passed on the straight section, had she not kept speeding up each time I tried). Once you call "on your left", you have the responsibility to complete your pass as quickly and efficiently as possible, and they have the responsibility to make that possible. I have said "on your left, please, when you get a chance", in areas where I need to pass but recognize that it won't work right there.

I don't use it out training, because it seems a little over-the-top, plus little old ladies tend to fall if you startle them. So I try to gently make my presence known, slow up behind them and wait if it makes sense to, etc. Sometimes it can be frustrating, but better than being rude.

As I said, I've never used it riding, but it seems like the same rules would apply. I can see how, in a more populated area with lots of riders/walkers, or on a MUT, it would be a good tool. Where I am, it seems like it would come off as elitest or something, and maybe somewhat demanding.

Anybody remember Taea Leoni (sp) in Spanglish? From 50 yards back , "ON YOUR LEFT!!". I thought that was pretty funny.

Oh - the OP's question: to me, it means to get over as soon as I safely can to make room for them to safely pass, inconveniencing them as little as possible.