The slippery slope fallacy occurs when an arguer presumes that because it is possible to imagine a current situation continuing, expanding, or extending until it brings about a more extreme situation in the future, that therefore it will do that.

Here is an example:

Mom: "Can we get the kids tickets to the circus, like they've been begging for?"

Dad: "No, because if we do that, then the next thing you know, we'll be getting wrangled into getting them tickets to Broadway, then a rock concert -- then plane tickets to Hawaii!"

Dad is committing the slippery slope fallacy. Although it is possible to imagine the series of events taking place that he describes, he offers no evidence that it actually will take place.