The setuid feature enables an executable to be run with the effective UID of the file owner. For example, a binary owned by root (passwd) can be run by any user (so they can change their password). Normally, simply giving group-level execution rights isn’t enough. Because while you might be able to run passwd, it will still fail when it tries to modify files not owned by the invoking user.
With setuid, the running process will appear to be running as the file-owner (hence the term effective UID). This ensures that the program can indeed modify files also belonging to the owner. The best-case use for this (and probably most common) is for root, when it wants to make binaries and services available to users like the change-password facility that also must make file-system changes to root owned files.
Command
chmod 4<permissions> <filename> (the 4 prefix means to apply setuid)