As players get older it's harder for them to learn. Their skills will be harder to improve and eventually they will even decrease.
Each player has an age factor. This is a percentage of 100% for young players that goes down as players grow older.
The actual skill of a player is calculated by multiplying the number of training points with the age factor and dividing this by 20. For example: a player with 80 training points passing and an age percentage of 88% will have a passing skill of 80*0.88/20=3.52 balls.
You can find the training points in the training complex on the page where you can spend your player's experience points. You can find the age percentage in brackets after the age of your player, for example when you go to "players" in the menu.
You don't need to understand these formula's. What's important to understand is that the skill of a player starts to slowly decrease after a certain age. At first this decline will be easily compensated by training, but since training points becomes more expensive when your base skill is higher the training will slow down. Eventually your player will get worse over time and will have to be replaced by a younger player.
In practise players can probably be improved till they are around 29-30. After that age they may still be useful for a while, but they are not likely to get better and will probably even get worse. Keepers can stay useful a bit longer.
Speed, Power, Dueling, Passing and Scoring are all affected by age. Endurance is affected twice as much (so the real endurance is (base)*(age)*(age) instead of the normal (base)*(age). Blocking is only slightly affected. This is the reason keepers can compete at older ages. Tactics and talent are not affected.