If P (x) is a polynomial of degree n then P (x) will have accurately n zeroes, some of which might repeat.

This fact says that if you list out all the zeroes & listing each one k times where k is its multiplicity you will have exactly n numbers in the list. Another manner to say this fact is that the multiplicity of all the zeroes has to add to the degree of the polynomial.

It will be a nice fact in a couple of sections when we go into detail regarding finding all the zeroes of polynomial.  If for a polynomial we know an upper bound for the number of zeroes then we will know while we've found all of them and thus we can stop looking.