Each of the training bags is designed to look like a Pokemon with that base stat being particularly high, and are all organized into evolutionary lines. They are as follows
HP:
-Small: Azurill
-Medium: Marill
-Large: Azumarill
Attack:
-Small: Machop
-Medium: Machoke
-Large: Machamp
Defense:
-Small: Aron
-Medium: Lairon
-Large: Aggron
Special Attack
-Small: Litwick
-Medium: Lampent
-Large: Chandelure
Special Defense
-Small: Flabebe
-Medium: Floette
-Large: Florges
Speed
-Small: Zubat
-Medium: Golbat
-Large: Crobat
As for the team flare bag, it reduces the number of hits required to break the next bag you use.
Source