The maximum generations parameter is set up in the backup set properties, and it must be a number between 1-9999. This means that this backup set will save up to this maximum number of restorable generations on DS-System online storage. It will not keep more than this number on the online storage (when it reaches the limit, the oldest generation is overwritten). Overwriting is done during the backup process and does not take into consideration any retention rules that might apply, since retention is a separate process

The best uses for maximum generations are:

All cumulative backups (on-demand and scheduled) will keep up to the maximum generation number. If a low number of maximum generations is configured for a scheduled backup set, be aware that if you run an on-demand backup, what is kept online might not be what you expect.

For example, you create a backup set with maximum generations set to 7, and schedule it to run daily (to keep the daily changes for a week). Assuming all backup files change daily, you expect one generation for each day. If an on-demand backup runs on this set, it might disrupt the pattern, giving you 2 generations from the same day, and restorable generations going back 6 days, instead of 7. (This assumes that the file changed before the on-demand backup, and before the scheduled backup.)