Next enemy mode is listed in bottom left of the game screen.

Normal enemies go at a normal speed and have normal hp
Hard enemies go at normal speed and have some extra hp
Fast enemies go at fast speed and have slightly less hp
Immune enemies go at normal speed and have normal hp but take no damage from magic towers (which are ice, fire, and arcane towers)
Bosses enemies go at normal speed and have tons of hp and give extra gold and score