It depends on the context. When someone talks about a string being null-terminated, they usually are talking about a C-style string, which is simply an array of characters, followed by a 0-byte at the end, sometimes refered to as \0 or null.
This stands in contrast to string datatypes which instead store their length at the beginning, and then an array of characters. In this case, the string "yo!" would be represented as:
Length Char0 Char1 Char2
------ ----- ----- -----
3 y o !
When someone talks about a string "not being terminated", they're usually talking about a string that is not enclosed by two sets of quotes -- this is the kind of error a compiler will give you. It's a totally different thing.