A suid or set uid program/script is an executable that has the setuid bit set via chmod +s binary name see chmod(1). The setuid bit will mean that when the program runs it will change its 'effective' user id to the user that 'owns' the file on the file system see chown(1). The running binary will aquire the permissions of that user. So if root 'owns' the file (see chmod) then yes when the binary runs then it will get root permissions, if however fred owns the setuid binary then when it runs it will have freds permissions.

Thre is also a setgid (set group id) this does exactly what you would expect from the definition of setuid.

The setuid/setgid bit has different meanings if set to non-executable files check out the manual page for chmod for more details.

HTH.
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Zigster