Generally, it's done to control critter numbers to be in ballance with their habitat, and secondly, public safety.
The main reason is that there are times of year critters are breeding/raising the next generation and shouldn't be disturbed. If they were their numbers may fall below sustainable and the ecosystem is impacted by that loss.
In States with tough Winters, once winter sets in, the bioligists know there will be a certain percentage of non-migratory critters that will die-off during the Winter due to predation and lack of food. Such as 20% for Deer here in NYS. To better match the critter numbers to the carrying capacity of the land (food and shelter) setting season dates and bag limits to only take the Winter die-off percentage is a good way to keep the number of critters in closer ballance with their habitat.
Sometimes that way gets out of wack, like the high numbers of small game we had around these parts last Winter. However, long term it equals out and works rather well.
Another factor is safety when there may be other seasonal recreational use of an area such as not allowing hunting in some areas during fishing and camping seasons. Many of the state lands around here allow both hunting and camping in the same areas, but not at the same time of year.
Paul.