It's a phase angle power control without hysteresis.
For an explanation, Refer Page 4 of
http://www.littelfuse.com/~/media/e...rol_using_thyristors_application_note.pdf.pdf
Incidentally, schematics can be drawn that can confuse viewers. I have redrawn the schematic which, I think, is easier to understand.
C1 R1 forms the snubber.
The Triac, Diac, R4, C2 and the Pot form the phase control.
D1, D2, D3, D4, R2 and R3 form the Hysteresis defeat.