Find a text string in a file and output only the rest of the text that follows it?

Use awk:

awk 's;/^three$/{s=1}' file

or

awk 's;$0=="three"{s=1}' file

• s; will print the line if variable s is true, which is the case first time after the pattern/word has been found ...
• /^three$/{s=1} will set variable s to true (1) if pattern/word is found.

With GNU sed:

sed 0,/three/d

Note that Linux is a kernel, it doesn't have utilities. GNU sed is the sed implementation commonly found on GNU/Linux systems like Debian GNU/Linux. GNU sed predates Linux and has been compiled to run on most Unix-like systems including most of those running Linux as their kernel. It is itself a Free, Libre and OpenSource re-implementation (with a few extensions including that 0 address) of the UNIX sed utility from the late 70s.