The (t-value|t-statistic) is a test statistic.
In NHST, it is essentially a ratio of what we observed relative to what we would expect just due to chance.
<MATH> \begin{array}{rrl} \text{t-statistic} & = & \frac{\text{What we observed}}{\text{What we get due to chance}} \\ \end{array} </MATH>
Each t-value has corresponding p-value depending on the sample size.
If I get:
In order to have a p-value of below 0.05 (which is quite significant), a t-statistic of about 2 is needed. At 16, the t-statistic is huge, it's very, very significant.
See Statistics - (Univariate|Simple|Basic) Linear Regression