What does embeddable mean?

[admin@saptasindhu.website <admin@saptasindhu.website>]

I understand that Lua is a scripting language, and hence has an interpreter, most probably with an in-built compiler (like Perl).

I fail to understand what is meant by Lua being embeddable.
Does it mean that the Lua interpreter (which is written in C) can be included in a larger C program?
If yes, does that mean the larger C program can then run Lua scripts while the larger C program is running?
If yes again, how do those Lua scripts being called from the larger C program get access to that C program's functions?
For example, I can understand that a stand-alone interpreter for a scripting language would have a systems programming interface which exposes the low-level routines (like POSIX or WinAPI) to be used by that scripting language.
But, I cannot understand how a embeddable Lua interpreter could be useful?

Best regards.