“Cheers!” can be used while toasting, where it is equivalent to Salud! Down the hatch! Santé! Indeed it is, me old cock, and long may your big jib draw! etc.
But there is another use, purportedly equivalent to thank you “when giving or receiving something”. Wait. When giving? Who says thank you when giving something?
A: Do you have any gum?
B: Here. Cheers!
A: Can you send me the client’s contact information?
B: As requested: email@example.com Cheers!
Clearly, “Cheers!” is not equivalent to thank you in such cases. Indeed, it basically means “Thank me!”
I suppose it’s useful to be able to use the same word regardless of whether I should be thanking you or you should be thanking me. For example, I’ve noticed myself saying “it’s all right” in such a way (’sarrigh’) that it sounds the same as “sorry.” This is useful if it’s not clear, as when bumping into someone on the bus, whether I should be apologizing to him, or he should be apologizing to me. And since he’ll likely be saying the same thing at the same time, it works whether his ’sarrigh’ comes before or after my ’sarrigh’.
“Cheers” in its non-toasting sense seems to have been brought to Canada from England or Australia, maybe in the 1980s when Paul Hogan, a.k.a. Crocodile Dundee, was introducing “No worries” and “Another shrimp on the barby.” If it has stuck better than “G’day, mate,” there remains something un-Canadian about it, though not quite to the extreme of substituting “Uh-huh” for “You’re welcome,” which can only have come to Canada from the south.
One engine of the popular Canadian adoption of “Cheers” when giving something must be its pervasive use in the restaurant industry by servers bringing drinks to a table. Interestingly, in this context, the two meanings are conflated: the server, while “literally” uttering a customary giving-something-to-someone phrase, is able to implant the unconscious fantasy that she’s having a drink with you.
Another probable reason for the ubiquity of “Cheers!” in the service industry, even when just bringing food, also has to do with tips. Since “Cheers!” obviates the need to say “Thank you” in the interaction, the poor Canadian is left, at the end of his meal, with cheque in hand, feeling deprived of having had sufficient opportunity to thank his server. As his luck would have it, he now has a concrete means of doing so.