League of Legends (LoL) Question: Mechanics?

Not really sure what you mean by "mechanic champions," but the term mechanics often refers to the micro controlling of your character. champions that require good mechanics are ones that have a more complicated kit or require more micro-intensive control ( eg: Lee Sin, Riven are more mechanically intensive than Annie).

Mechanics intensive champions are champions that have a complicated kit that requires good timing and accuracy to succeed. Champions like Annie and Ryze are not so mechanically intensive; With these champions you just kinda cast your spells, whenever they're off cooldown. Champions like Lee Sin, Riven, Zed, LeBlanc, Ahri, and maybe even Thresh are considered very mechanically intensive. All champions have some degree of mechanics. For instance, a good master yi can Alpha Strike at the right time to fizzle a Death Mark, or any other spell with a projectile speed.

As a general rule of thumb, immaculate play with a champion with a mechanically intensive kit often yield greater potential for carrying your team. On the contrary, blundering with a mechanically intensive champion is quite easy to do, and can be punished harder than a non-mechanically intenisve champion