Hexproof is not really a new mechanic, it has just been given a keyword name starting in Magic 2012. It ha been around for year and cards from the past have had their official text changed so they now have hexproof.

Hexproof means that the permanent cannot be targeted by spells or abilities that are controlled by the opponent’s of the controller of the permanent. For example, Troll Ascetic cannot be targeted by your opponent’s Doom Blade, but it can be targeted by your Titanic Growth.

While permanents with hexproof cannot be targeted, they will still be affected by spells and abilities that do not target like Pyroclasm or Day of judgment. Also, abilities like Gatekeeper of Malakir‘s enters the battlefield triggered ability do target, but they do not target creatures in play. A player can be targeted by this ability and choose to sacrifice a creature with hexproof they control.

Finally, as hexproof only affects opponents, in multiplayer games like two-headed giant your teammates can target permanents with hexproof that you control.