By simple definition, a paradox arises when there is a contradiction in a statement, situation or in a thing.
In this case, "The following sentence is true[we will call this Sentence A].
The previous sentence is false [Sentence B]", meets this criteria in a few ways; 1) if Sentence A is true, then Sentence B is also true. But then that means that Sentence B, "The previous sentence is false", makes Sentence A untrue.
2) If Sentence B is true, that makes Sentence A not true. And then it all goes around and around.
A paradox isn't meant to be solved, more so, meant to be discussed, argued and philosophized. It's meant to make you think really deeply about the statement and that is what those two sentences do, meeting the last criteria of a paradox.
So, in summery, "The following sentence is true.
The previous sentence is false", is a paradox because it is contradictory and it makes you argue and philosophize about the deeper meaning of the statement.
Hope that helps and don't worry if you're confused. All paradoxes are confusing.
