while(batting_record!='/n');

What does this mean?

while the input data is not a new line? or a / character n?

'/n' will cause a compilation error.

Within a character constant or a string literal, character sequences starting with a \ (backslash, not forward slash) are called escape sequences. The escape sequence \n (backslash followed by an n) represents a newline. So, '\n' is a single character, and "\n" is a string literal consisting of two characters, one with value '\n' and the other zero.

Note that \n is not the only escape sequence. Any basic C text will describe them, or (noting that you should sanity-check most things you find on the internet, including this post) Google for "C escape sequence"

This is, in all likelyhood, a programmer mistake (she must have wanted a backslash and the absence of the semicolon).

As it is, it's either an infinite loop or a do nothing statement depending on the value of batting_record.
If batting_record has a value of '/n' (a multi-character constant which value is implementation defined) it is a do nothing statement
if batting_record has a different value it is an infinite loop: doing nothing (empty body) does not change the value and all it does (over and over and over) is compare the values.

Code:

---

int batting_record;
while (batting_record != '\n') {
    batting_record = getchar();
}

---

This code, on the other hand, keeps reading characters from the standard input stream up to and including a newline character. Note that this code does not check for errors, as a proper code should do.