I agree with most of what cowboy says. I think most people have more or less the same definition of atonality *in concept*, but hardly in their ears. If we were to say simply that an atonal piece had no discernable tonal center, then we'd have to examine how discerning our ears were. Perhaps we should base the definition on how far the composer has strayed from "conventional" western harmony practice, but then we'd have to decide where the convention ended, as opposed to where it was simply extended. Very sticky stuff.
In any case, Le Sacre is very tonal to my ears, even where it is extremely dissonant. By contrast, take his later Agon... it is much less tonal (except for the first and last sections), but much less dissonant. Or take Petrushka... even some recognizable keys in there, though they are sometimes used two at a time, especially C and F#.
It's all a matter of degrees.