When someone asks when does fishing season start, they could be inquiring about three different things. When can you legally target/harvest a fish species, when will the fish be biting, or when will a migratory fish come around?
Legal fishing seasons vary by locale and species. Some species are open all year long with no restrictions on when you can fish for them or harvest them. Some regulations prohibit the harvest of fish during certain times of year. Even stricter regulations exist where you can't harvest or catch and release at certain times of the year.
When will the fish be willing to eat bait or hit a lure is another key piece of information for anglers. Since fish are sensitive to changes in water temperature some species of fish will enter a state of torpor when temperatures are too low. Different species of fish can acclimatize to various ranges in water temperatures, so choosing an appropriate time of year (in terms of water temperature) is key. Outside of just temperature, fish that spawn or migrate at certain times of year may also not be willing to eat bait or hit a lure during those periods.
Some fish species (mostly saltwater species) migrate far distances. You can't catch what is not there so knowing if your target species is migratory and the migration pattern is necessary information. There is no universal pattern for migration and the time windows for angling can range from mere hours to weeks.
Fishing Fundamentals