Here is what the bash documentation says:
PS1 The value of this parameter is expanded (see PROMPTING below)
and used as the primary prompt string. The default value is
PS2 The value of this parameter is expanded as with PS1 and used as
the secondary prompt string. The default is ``> ''.
PS3 The value of this parameter is used as the prompt for the select
command (see SHELL GRAMMAR above).
PS4 The value of this parameter is expanded as with PS1 and the
value is printed before each command bash displays during an
execution trace. The first character of PS4 is replicated mul‐
tiple times, as necessary, to indicate multiple levels of indi‐
rection. The default is ``+ ''.
PS1 is your normal "waiting for a command" prompt,
PS2 is the
continuation prompt that you saw after typing an incomplete command,
PS3 is shown when the
select command is waiting for input, and
PS4 is the debugging trace line prefix.
The documentation I quoted doesn't say so, but the default for
PS3 in bash is
$ select x in foo bar baz; do echo $x; done