What is tetrahedral site?
Here is a good explanation with clear sketch.
Following description and figures are taken from
https://www.tf.uni-kiel.de/matwis/amat/def_en/kap_1/illustr/t1_3_4.html
"In a tetrahedral site the interstitial is in the center of a tetrahedra forms by four lattice atoms. Three atoms, touching each other, are in plane; the fourth atom sits in the symmetrical position on top. Again, the tetrahedral site has a defined geometry and offers space for an interstitial atom."
"The configuration on top is the tetrahedral position in the fcc lattice. The black circles denote lattice points, the red circle marks one of the 8 the tetrahedral position."
"The picture on the bottom shows the tetrahedral configuration for the bcc lattice. We have (6 · 4)/2 = 12 positions per unit cell."
Figure: The tetrahedral site in FCC (above) and BCC (below) crystal structures
References
https://www.tf.uni-kiel.de/matwis/amat/def_en/kap_1/illustr/t1_3_4.html