From the manual

The better form a player is in, the better he will perform. It's not about the physical context though, it has nothing to do with how well trained a player is. Form in Hattrick reflects a combination of aspects making it possible for, or preventing a player, from reaching his full potential – like for example how his private situation in life is at the moment.

On the player page you can see a player's "current form". It's the figure applied for matches. An "excellent" player in "wretched" form is usually worse off than a "passable" player in "solid" form for example. Current form is negatively affected by the amount of stamina training in the team; the more stamina you train (percentage-wise) the more negative effect.

Additionally, there's a hidden "background form", which is used to compute where the player's form is heading. Each week, during training, the current form of every player will change, moving towards the hidden background form. Current form is not changed immediately to the figure of background form. Instead it moves in steps over several weeks, though the further away from background form they are the larger the steps will be.

After current form has been changed during training, there is a chance that background form is changed for each player. Every player has the same individual chance of having his background form change, and there is nothing you can do to influence this chance. However, when chance decrees that a player's background form will change, there are several factors that influence what the new background form will be:

If a player has participated in a match during the week. This is very important!

Training intensity – the harder you train, the better form in general

Your coach – the better skilled he is, the better form in general

Form Coach - a Form Coach is specialised in improving form.

Assistant coaches – Assistants also help improve form