These characteristic is actually telling you how many Individual Values the Pokemon has. THe characteristic doesn't only mean that the IV is for a specific stat, it just indicates which stat is highest (if all IV's are 31, it will randomly indicate a characteristic)
Also, look Here to learn more about IV's and what the characteristics mean.
Anyways, here's how many IV's a characteristic indicates a Pokemon has:
HP
:Loves to eat 0/5/10/15/20/25/30
:Often dozes off 1/6/11/16/21/26/31
:Often Scatters things 2/7/12/17/22/27
:Scatters things often 3/8/13/18/23/28
:Likes to relax 4/9/14/19/24/29
Attack
:Proud of its power 0/5/10/15/20/25/30
:Likes to thrash about 1/6/11/16/21/26/31
:A little quick-tempered 2/7/12/17/22/27
:Likes to fight 3/8/13/18/23/28
:Quick tempered 4/9/14/19/24/29
Defense
:Sturdy body 0/5/10/15/20/25/30
:Capable of taking hits 1/6/11/16/21/26/31
:Highly persistent 2/7/12/17/22/27
:Good endurance 3/8/13/18/23/28
:Good perseverence 4/9/14/19/24/29
Special Attack
:Highly curious 0/5/10/15/20/25/30
:Mischeavious 1/6/11/16/21/26/31
:Thoroughly cunning 2/7/12/17/22/27
:Often lost in thought 3/8/13/18/23/28
:Very finicky 4/9/14/19/24/29
Special Defense
:Strong willed 0/5/10/15/20/25/30
:Somewhat vain 1/6/11/16/21/26/31
:Strongly defiant 2/7/12/17/22/27
:Hates to lose 3/8/13/18/23/28
:Somewhat stubborn 4/9/14/19/24/29
Speed
:Likes to run 0/5/10/15/20/25/30
:Alert to sounds 1/6/11/16/21/26/31
:Impetuous and silly 2/7/12/17/22/27
:Somewhat of a clown 3/8/13/18/23/28
:Quick to flee 4/9/14/19/24/29
Basically, for individuals:
31 HP: Often dozes off
31 Atk: Likes to thrash about
31 Def: Capable of taking hits
31 Sp. Atk: Mischevious
31 Sp. Def: Somewhat vain
31 Spd: Alert to sounds