At it's simplest (and extreme), game spoilers are the equivalent of telling someone the ending of a movie or sub-plot outcome of a series episode (or similar).
A more common (and mostly with well intentions) example however is this:
We've seen and know we can explore all containers while playing The Elder Scrolls: III Morrowind (whether owned or otherwise). Someone in chat says "Check all the containers in this game, it will serve you well ;)" while knowing there's nothing major to be found in the current property we're searching, s/he knows however that doing some may help the player (& viewing experience) find some awesome stuff later and perhaps catch a miss-able quest all without spoiling a thing! Genius!
Spoiler / Spoiler Tip
Again, we're exploring Morrowind in The Elder Scrolls 3, someone (excited and hopefully well-intentioned) says the following in chat "go upstairs, turn right, check the in the brown centre cabinet, there should be a magical broken unicorn. You need that to do a quest for Gay Bob!"
A) It's a little backseaty...
B) We've never even had the pleasure (or displeasure) of meeting a Gay Bob, much less knowing there's a quest for him.
C) I might as well be using a walkthrough with that level of overly specific intel. Now again, it may be with well intentions, but, please, curb your enthusiasm and try to avoid being 'that' dude/ete!