What does this option in Terminal do?
It seems to have no effect on anything.
Essentially, this option prevents other applications (including things like TextExpander) from "listening in" on what you are typing. By preventing other background processes from recording or accessing your keystrokes, you are ensuring they cannot be logged or monitored, eg. by a simple keylogger, or another program running with normal permissions for potentially malicious purposes.
Here is a screenshot from the help menu.
There's a great answer about it on the Security Stackexchange
"Secure Keyboard Entry" maps to the
EnableSecureEventInputfunction whose concept is described here. Basically, applications don't access the hardware themselves; they obtain events (e.g. about key strokes) from the operating system. Some elements in the OS decides what application gets what events, depending on its access rights and GUI state (there are details depending on which application is "in the foreground").