I retrieved all the average yearly temperature data from years 1899-2011 (113 data points in total) and plotted them and figured a regression line.

I'm trying to test the hypothesis that temperature went up for a certain area for the given time interval, but I'm not sure if I should even DO a test.

But I did get a sufficiently low p-value to reject the null, and my confidence interval only contained positive slopes, too.

But the regression line kind of already tells me that it DID go up.

What does the p-value for a regression test even tell us, anyway? How should I interpret it in context? Just like a regular t-test interpretation, like: "The chance of obtaining this slope assuming the null is true..." ?