If the y-values are just a random sample that does not depend on the
x-values, then the F statistic will be the ratio of two independent estimates
of the variance of y.
If the F statistic is too large, then you reject that hypothesis and
conclude that instead the y-value depends on the x-value, as described by the
regression model.
The p-value helps you quantify "too large"; p=0.05 means that if the
y-values really are just a random sample that does not depend on the
x-values, there was a 5% chance of getting an F as large as the one you
actually observed.
You are touching on concepts with implications that are not simple. I
recommend taking a class or reading a good text on statistics.
Jerry
