The woven braid around the head's edge that anchors the whole tensioning system.
The braided ring woven from the head's own skin at the pudi's circumference. The baddhi straps lace through it, so all the tension the head carries passes via the gajra — it is the structural anchor of the whole system.
It also matters in tuning: hammer taps on the gajra (downward to raise pitch, upward from below to lower it) are the fine adjustment between strap work and gatta moves. A gajra pulling unevenly shows up as a head that will not tune true around its circle.
Further reading
Rebecca Stewart, The Tabla in Perspective (PhD dissertation, University of California, Los Angeles, 1974).