To get Season currency when your hero's or team's ranking resets, you must play at least 3 battles during the Season with this hero/team. You must play at least 3 battles specifically in ranked battles.
Season currency is awarded for overcoming rating thresholds - milestones. Detailed information about rewards and rating ranges can be found within the game itself. The in-game hero library contains a detailed description of rating thresholds with their specifications and rewards for each milestone.

After resetting your rating and playing 3 battles in the new season, you will receive currency for all milestones achieved in the current hero/team rating.
Season currency can be used to make purchases in the corresponding section of the store. Season currency can only be obtained in Seasons. Season currency cannot be purchased or earned in other game activities. The contents of the Seasons store change every month.