The symbols you are referring to depict a player's so called specialities.
Specialities are divided into silver and gold ones, where gold ones are showing that the player is a really great talent. They are awarded for high stats in certain areas, for example the Speedster speciality is awarded to players with high acceleration and sprint speed (>= 90 I believe).
You can view the specialities for a specific player in the Team Management view:
Main Menu -> Customize Fifa -> Edit Teams -> Team Management -> Select a team -> Squad -> Select a player with a speciality -> press LT
Notice that only the best 3 specialities are shown in the team overview, in the below example you can see that C. Ronaldo actually has more than those 3:
The following list of specialities is assembled by hand, so it might be incomplete or contain errors.
The Acrobat uses his athletic ability to get to balls that other players won't get to. This player does many acrobatic clearances and bicycle kicks.
Clinical Finishers have the technique required to be deadly goal scorers from anywhere within 25 yards. They have an eye for the goal, and will make you pay for your mistakes.
This player is excellent at swinging the ball in from the wing. They are accurate, serve the ball with pace, and can bend it around defenders into dangerous areas.
This player not only has a powerful shot, they are accurate from distance. If you get the ball in open space, don't be afraid to take a pop at goal.
This player has excellent ball control and is great at getting around defenders. He will also likely have a few tricks up his sleeve and will use them to beat his opponents.
FK specialists have spent countless hours on the training ground taking free kicks. Some will be able to curl the ball around the wall, some will get it up over the wall and back down.
This player has exceptional ability to distribute balls to his teammates. On the ground or through the air, he is the guy you want to play through to create chances.
The Poacher excels in Finishing inside the penalty area both with their feet and with their head. They have the ability to turn half chances into goals.
A speedster is a player who can not only get off the mark quickly, but also has a very high top speed.
Players with the Strength speciality are forces to be reckoned with. They are difficult to push off the ball and use their size and strength to their advantage when defending.
Tacklers have mastered the art of dispossesion. They react quickly to the situation to read the dribbler and are able to break up more plays than the average defender.
This player is fantastic at reading the game defensively. He will excel at reading the trajectory of passes, and will react faster off the mark to intercept passes.
This player is multitalented and excels in a number of key areas of defending, making him the complete package in terms of defending.
This player is multitalented and excels in a number of key attacking areas, making him the complete Forward package.