the thrombin site is not refer to the thrombin protein but to presence of a DNA sequence with codify for the recognition site for cleavage with thrombin.
Is quite common if you would like to fuse TAG (eg HIs, MBP, GST, Trx, GB1) to the N-term of your recombinant protein to improve its expression, solubity or purity, the addition of a protease (as thrombin, TEV, Fatt.Xa...) to allow you to remove those tags at the end of purifciation process.
On my blog: ProteoCool https://proteocool.blogspot.com/
at PAGE 2 you can find a video tutorial
ProteoCool n°22 (Overview on Tools for recombinant protein expression in E.coli )
where you can find a section dedicated to protease cleavage.
Thrombin is a protease. "Thrombin site" as labeled in the picture is the DNA sequence which contains the recognition site of thrombin. After purification of induced proteins carrying an affinity tag like 6-His/MBP/GST at their N-terminal end, thrombin is used to cleave the affinity tag.