Regular maintenance items would be things like rebuilding caches, upgrading software and/or templates, doing some data trawling for statistics, various routine maintenance tasks like backups, (which work better on quiet systems) and a variety of other expensive, infrequent tasks.
Some tasks just require pouring over a lot of data, and it's not really efficient to do after each change. Recommendation databases are one thing that comes to mind, as you don't need up to the second data, and it's rather expensive to calculate common purchase patterns across many different users. This is an N^2 complexity problem with some algorithms, and tends to take both a lot of data trawling, and lots of memory.
Financial institutions may use the down time to calculate and make interest payments to accounts, or close outstanding transactions and calculate reconciliation balances. This data in theory should never change after reconciliation, so it makes sense to write it to WORM storage at this point.
Backups are a major item that's often done during downtime because high Disk I/O tends to bring even very powerful servers to their knees, and taking the site offline can help speed the backup process. I remember one organization I was at, where they had a very large customer RAID array, and the backup team kept complaining because their backup window for this one customer typically extended 22-24, and at one point 26 hours. A small amount of quiet time can decrease that window substantially.