If the difference between means is greater, t is greater. If either standard deviation is smaller, t will be greater. If n is greater, then t will be greater. The greater each of these quantities is, the greater is our confidence that the true means are different.
If we calculated a t statistic by hand then we would go to a table of critical values and compare the t statistic with the tabled values. From the table we would then read a probability (p value) that the null hypothesis is true. A computer program typically returns the probability value itself without your having to resort to a table. Now go back and read the second sentence again. In a two-sample test the p value is the probability favoring the null hypothesis. This point even befuddles experienced researchers who don't use statistics very often. Let's see if you have it figured out.
A t test comparing data sets A and B returns a p value of 0.24. A t test comparing data sets C and D returns a p value of 0.03. For which pair of data sets are we more confident that the populations are different?
A and B
C and D