There are 3 game modes : Creative, survival and multiplayer. Survival and creative can be made freely but multiplayer must be done on a server.
Creative has only yourself as mobs.In creative you don't need tools to break items and break almost instantly. Creative has tons of blocks exclusive to it's mode.Concepts are left out entirely from this mode.
Survival has yourself,Chickens,sheep,Cows,Turkeys,Pigs,Wolves,Spiders,zombies,dogs,cats and pumpkin heads as mobs.You need tools to break things and sometimes the item won't drop if a tool isn't used.You can die easily in this mode and have items in your inventory unlike creative.Concepts are big in this mode.
People are the only mobs in this mode.Sometimes people prevent you from breaking or placing blocks.Be aware on what you're doing because you can get a report out of nowhere.You can chat in this mode.