It's not quite clear which p-value you are asking about, but I'll assume it's the Pr(>|t|) values in the last column.
Those are p-values for the two-sided test of whether that coefficient is equal to zero. If the true value of the coefficient is zero, expect a random value approximately uniformly distributed between 0 and 1.
Those small numbers "< 2e-16" aren't very likely from a uniform distribution, so the classical interpretation is that there is evidence that those coefficients are non-zero.
On the other hand, 0.0986 isn't all that unusually small, so that one might really be zero.
