Pi-Hole maintains a gravity list (list of domains to block), which is constructed from all the block lists to which you subscribe (public lists), along with your whitelist. A cron script updates the gravity list weekly on Sunday. If you mouse and hover over the "Domains on Blocklist" box at the top right of the Admin GUI dashboard, you can how long it has been since the gravity list was updated.
You can update the gravity list manually with pihole -g from the command line, or from the Web GUI > Tools menu. This is normally not necessary unless you change your blocklists or have a problem.
Pi-Hole does not automatically update itself (the software). The Web GUI will tell you when a Pi-Hole update is available, but you must manually update Pi-Hole with the command pihole -up from the command line.
If you run a debug log, the cron scripts will be listed, as shown below:
-rw-r--r-- 1 root root 1496 Aug 5 19:08 /etc/cron.d/pihole
52 3 * * 7 root PATH="$PATH:/usr/local/bin/" pihole updateGravity
00 00 * * * root PATH="$PATH:/usr/local/bin/" pihole flush once quiet
@reboot root /usr/sbin/logrotate /etc/pihole/logrotate
*/10 * * * * root PATH="$PATH:/usr/local/bin/" pihole updatechecker local
54 12 * * * root PATH="$PATH:/usr/local/bin/" pihole updatechecker remote
@reboot root PATH="$PATH:/usr/local/bin/" pihole updatechecker remote reboot
Other scheduled tasks including rotating the pihole.log every night, etc.