Hidden attributes of a player can be revealed by scouting a player. Scouting your own players are free, but a nominal fee will be charged for scouting players in other teams.
Potential determines how high the overall attributes of a player can go upto. If a player is low on current ability but has high potential, it means he can be developed very well by training properly.
Learning attribute helps a player to pick up skills faster during training. A good learner will be able to fulfill his potential faster, while a bad one will struggle to improve no matter how good your coaches and training facilities are.
This determines how aggressively a player tries to win back balls when not in possession. Although this serves well to get more possession of the ball during a match, it is also likely that the player might go into 50-50 challenges and give away fouls for his opponents.
Leadership determines how good a player is in leading the team. Having a good leader on the pitch boosts the overall performance of the team.
Flexible players can play out of their natural positions if they have the skills to perform in those positions. So if you are playing players out of positions for any reason, make sure they have good Flexibility attribute.
Flair is the ability of a player to produce the unexpected. It might be a smart use of the legs to get away from his marker, or a key pass out of nowhere, or a shot at goal from a really tight angle. Even if it is mostly good for attacking, it might be useful for all players.
Right foot and Left foot
This determines which foot the player uses mostly. When deciding which side of the pitch you are deploying a player, you should consider his stronger foot. A right footed attacker might be able to provide better crosses when played on the right side of the pitch, but it might be harder for him to cut inside and move towards the centre if his left foot is weak. Similarly, a right footed defender will be able to tackle better on the right side while harder to intercept passes or stop a player moving towards the centre of the pitch from the right side. So decide where to play your players based on your own tactics and your opponent's players.
Other Hidden Attributes
These attributes can be observed only by reading match reports, and keeping track of which matches a player performs/does not perform, how often he gets injured etc. Observation and experimentation are the only ways of finding out attributes which are not revealed by a scout.