To begin with a player has four sets of abilities, Fielding, General, Hitting and Pitching. Each of these are divided into subcategories ranging from 1 to 100, 100 being the best, normally (always an exception).
Overall is a WIS general rating that is normally overinflated and sometimes underinflated. Most ML capable position players and starting pitchers have a 70 or better while pen pitchers and backup role players are in the 60's. Not a hard rule however.
Range: Determines the movement ability of the player at a position. Higher the range the better he can play sophisticated positions such as SS or CF.
Glove: Determines how well he can use the mitt in fielding the ball.
Arm Strength: Determines how fast and a what speed he can get rid of the ball.
Arm Accuracy: Determines how accurate the throw is.
Pitch Calling: Catcher ability of how well he can handle the pitcher and his pitches.
All of these work together in the players overall ability to field a position. If you go to GM's Office - Roster Management - Edit Rosters and click on the position players position indicator it will open a card that shows the minimum abilities for each position. You can also change the players position from here if desired. There can be some give and take in the abilities as to whether a player can play a certain position or not. However I wouldn't go much lower than recommended in most cases.
NOTE: Never put a left-handed thrower in the infield except at 1B.
Durability: Used to determine when a player starts to fatigue and used in the recovery process of pitchers after pitching. A player with a durability in the mid 80's and higher, you don't have much to worry about. However, under that they will need a day of rest every now and then. Rule of thumb - a player with an 80 durability needs about 10 days off during the season while a 70 needs 30.
Health: This is one we have learned to hate over the last 6 or 7 seasons. Used to be that a health of 75 or better rarely got injured and those below had a good chance of being injured and below 60 almost always found their way to the DL. Now it is like a turkey shoot and a high training budget helps but not an end all to the problem.
Speed: Determines how fast a player is. Helps if you want to steal bases but must have a good base running ability also.
Patience: This helps in training and demotions and maybe waiting for the right pitch.
Temper: This is the exception as it is better low than high. Umpires tend to throw players out of games..hint hint hint
Makeup: Used in injury recovery and to stave off old age..lol..I am not joking.. has some other uses also but not greatly important if you ask me.
Contact: How well a batter puts the bat on the ball. A ball in play is always better than a strike out.
Power: Higher the number the more extra base hits...errr home runs
Splits: How well a batter fares against pitchers.
Eye: How well a batter sees the pitch.
All of these combined determine what happens during an at bat. A high Eye, Splits and Contact will cause a lot of walks also. A low Eye and High contact is not a bad thing and is quite common. Low Contact usually causes more strike outs.
Base Running: How well a player understands base stealing concepts used in conjunction with speed. High speed and low concept is not a good thing. I normally use 70 as a cutoff for both.
Bunt: self explanatory I hope.
Push Pull Tendency: Simple concept of where the batter is going to hit the ball 80% of the time. Over 50 is opposite field hitter.
Stamina: Determines how many pitches he can throw in an outing. Normally we like starting pitchers above 65. Durability is important as it determines how quickly a pitcher can recover after an outing.
Control: Determines how well he has command of his pitches. higher the better
Splits: Determines his luck (more or less) against batters. Higher the better
Velocity: How hard a pitcher throws. High velo is more of a strike out pitcher while low velo is a finesse pitcher. Both are good.
Ground Ball/Fly Ball: High is mostly a ground ball pitcher and low is fly ball. I run a good defense all the way around so it really doesn't matter but lean towards ground ball. Tempting fate is a fly ball pitcher in Coors Field.
Pitches: How well he throws the pitch. The type of pitch is window dressing. However the best thing is to have at least two good pitches in the first two slots (80,70). Most pitchers have there pitches graduated downward from good to throw away, when they are out of order tend to cause some problems.