Sorry if I sound stupid asking this, but what is meant by the expression "1 (mod p)", where p is greater than one? I'm sure it must make more sense than I can figure out.

If the context is important, I'm reading up on RSA, quote's here:
Let p and q be two different large primes. A large number p can be tested for primeness by applying Fermat's theorem, which states that if p is prime, then
a^p-1 == 1 (mod p)

for every positive integer a not divisible by p. (A double equal sign (==) is used instead of the usual symbol for congruence, which is not supported by all Web browsers.) A number p which passes this test for several hundred randomly selected values of a in the range (1, p-1) is almost surely prime.