Coefficients are the numbers that come before a variable.
For example, 5x. The coefficient is 5. Since 5 is an integer, it is an integer coefficient.
That's all it is: a coefficient that's an integer.
An not-example would be the 1/2 in 1/2x. Since 1/2 isn't an integer, it does not count as a integer coefficient.
Hope this helps!