From personal experience of over 6 years of MOBA gaming;
Easy AI matches are great to learn HOW to play the game. (For the super beginners)
They are also great way to easily and quickly take "First Win of The Day" Influence Points bonus.
Intermediate AI matches are a good platform to learn how to play a new hero. Use these games to learn how to perform the proper combo's with your hero of choice. To figure out just exactly how Elise's Rappel works, or Urgots Lock-On Missle Attack. These matchups are good also for map awareness and lane control. The bots perform ganking extremly well, linking together combo's with a precision that most humans have a hard time accomplishing. These matches are also good practice for warding, as if you ward properly you'll see the ganks coming and know your doing it correctly.
All bot matches are also good practice for last hitting minions.
Once those skills are down, I would move into Blind Pick games, which don't usually follow the meta, but will help you get used to playing against real people who can come up with new alternative stradegies on the fly.
AS SOON as your comfortable with all the previously mentioned factors, and have enough of a hero pool\ skill level to play ANY lane position, I would move into Draft games. Draft games are pretty much Softcore Ranked. They don't carry elo, but other than that they tend to follow meta-rules, and the players usually take themselves much more seriously. Draft games include bans, and round-robin hero picks. This allows players to learn how to counter-pick opposing heroes and how to properly ban heroes that either screw your team comp six ways to sunday or otherwise bring factors that you don't want to deal with into your game.
Obviously the final step is full on Ranked play, and you'll know when your ready for that. Or, you'll think your ready, and find out the hard way your not.
Play Bots on easy to learn how to play the game, and to earn IP points for first win of the day if you don't have a lot of time.
Play Bots on intermediate how to learn play specific heroes and last hit well.
Play Blind Pick to improve your game.
Play Draft Pick to polish your game.
Play Ranked to show others they need to play Draft some more. ;-)