The ones next to your player names are their 'form' or 'morale' values.
Red up arrow is best and means he is on fire and will be amazing.
White down arrow is the worst.
Players not on Red or yellow tend to lose their fitness/stamina bars much quicker and will need to be subbed off sooner.
Players on red are more likely to score on target and make better passes. I believe free kicks are affected too.
I scored 4 goals with Beckham from outside the area in one match when he was on red.
Their skill value for some stats are supposed to be altered based on the arrow with red improving them and green being the standard.
All this is what I have heard and read.
Choosing the keeper on a better arrow is a good option.
But then you have to consider, is it better to play Beckham on a blue arrow or Sinclair on a Yellow?
Answers on a postcard please!