Auto Setlists are setlists that build themselves. Instead of adding songs by hand, you define a set of criteria (e.g. "all approved songs", or "anything tagged #encore that I haven't played at The Kings Head") and Setlist takes care of populating the list. As your song library changes, the auto setlist updates with it.
Every band gets three Auto Setlists out of the box, one for each song state - Approved Songs, Practicing Songs, and Backlog Songs - all sorted alphabetically by song name. You're free to rename them, change the criteria, delete them, or add your own.
As an example, here's how the "Approved Songs" default Auto Setlist is defined:

You can delete these, change the criteria, or create your own by visiting the Auto Setlists tile in your band homepage. Here's a couple of quick examples to show how this can be useful - How about an automatically updating setlist that shows you songs that have been stuck in your backlog for more than two months:

Or maybe you want to keep it fresh with some "easy wins" for an upcoming gig. You can select approved songs that don't require any changes (or match any other tags you use) that you haven't yet played at a venue:

There are two places to look:

Each Auto Setlist is made up of one or more filter rows, all chained together with logical AND. So a setlist defined as "State equals Approved AND Tag equals #encore" will only show songs that match both conditions.
Below the filters, you pick how the matching songs should be sorted.
So, in summary: filters narrow the list, sort orders it, and the result is what you see when you open the setlist.
Each filter row has three parts: the field you're filtering on, the operator, and the value. The operators available change depending on the field you pick.
Match songs by their workflow state (Backlog, Practicing, Approved, Retired, etc.).
Useful for things like "everything we've approved" or "anything that isn't retired".
Match songs by one of your band's tags.
Combine multiple tag filters with AND to build up specific selections, e.g. "tagged #covers AND not tagged #drop-tuning".
Match songs by the artist field.
Comparisons are case-insensitive. Contains is handy for grouping a prolific artist together without worrying about exact spelling so "contains Bowie" will catch "David Bowie" as well as "Bowie & Queen" (Yeah, you know the song. Can tell I'm a Bass player 😉).
Match songs by how long ago they were added to the library.
This is what powers the "stuck in the backlog" example above. Pair it with a Song State filter to find songs that have been sitting in a particular state for a while.
Match songs by whether they've been played at one of your band's venues (linked via events).
Songs count as "played at" a venue if they appear in any setlist attached to an event at that venue, including upcoming events. Great for building "fresh material for tonight's gig" -type lists.
Pick a number of songs at random from whatever the other filters left behind.
Unlike the other criteria, Random Pick doesn't narrow the list down to songs that "match" something, it samples from the result. Chain it with other filters to do things like "pick 5 random songs where state is Practicing" for a daily warmup list, or "pick 10 random songs tagged #covers" to keep rehearsals varied. The selection reshuffles every time you open the setlist, so you'll get a different set of songs each visit.
Only select a given number of matching songs that match the criteria. Applied after sorting, so can be used to build queries like "approved songs, sorted by descending score, select 10" to give a top-10 list of most popular songs.
You can sort matching songs by:
For everything except Random you also pick Ascending or Descending. Random ignores the direction (because there's no meaningful "up" or "down" for a random shuffle).
When you open an Auto Setlist you'll get the usual setlist view, with one fixed set called "Auto Set 1" holding the matched songs. A few buttons behave differently though, because the contents are generated on the fly:

What you can't do is edit the songs directly, drag and drop to reorder, add extra sets, or delete the setlist contents. The whole point is that the list is defined by its criteria, not by a fixed list of songs. If you need to make manual tweaks, clone it first.
As the auto setlists are generated dynamically, you can't edit them directly or drag & drop to change the order of the songs. You can however clone the setlist (either as a personal setlist, or band-wide) which turns it into a regular editable Setlist.