If your training complex is at least level 3, you get the option to select a special training for one of your players. This training takes time, sometimes a lot of time. The higher the level of your training complex, the faster these trainings are completed. Special training usually also costs experience points and/or credits.
The cheapest training is to train a player to play on a different flank. Once completed, the performance of your player on that flank immediately goes up.
You can also train a player to play on a different position (eg. as defender, midfielder etc). This type of training removes some of the position experience of a player from all positions and adds it to the selected position. It also converts some points of the player's trainable skills back into experience points. Basically, this allows you to retrain (for example) a midfielder to be an effective defender.
A third type of special training allows you to improve the fixed skills endurance, speed and strength of a player. They are called fixed skills because they can't be improved by regular training. The effect of fixed skill training becomes less once players become older.
The last type of training is special attribute training. There are a number of special player attributes in the game, some of which can't be trained like "tall", "selfish" or "unpredictable", but some can be. You can find out for yourself which special attributes become available on the next level when going to your training complex. When you hover your mouse over a special player attribute somewhere in the game it will explain what it means.
Training special attributes has one significant difference with the other types of special training. For each trainable attribute your player already has, the next training will take 50% longer. This makes it increasingly expensive to train the same player on several special attributes.