When a player plays matches he will get tired. When you play only league matches you will probably not have to bother much about fatigue. When your team starts getting far in the cup and maybe even play champions league you will get more than one match a day and it may become a challenge to keep your players fit enough.
How tired a player gets depends on the following factors:
The base fatigue for a match depends on the number of minutes a player was on the field and the number of times he moved to a different region. Being an unused substitute does not make a player tired.
The higher the endurance of a player, the less tired he gets.
The type of match may also affect the amount of fatigue a player receives. Friendly matches and interlands make players less tired. Champions League and competitive matches for the national team make players 10% more tired.
Tired plays perform less in matches. A low level of fatigue has almost no effect on the player, but when the player gets into the yellow or red zone of the fatigue bar the effects will be noticeable.
A player that is very tired also has an increased chance to get injured.
The actual fatigue of a player is updated during the match. This means players with low endurance or who started the match tired may get into the yellow or red zone during the match.