MATT stands for “Merklize All The Issues” referring to the utilization of Merkle bushes in present and presumably future covenant proposals (opcodes, fraud proofs and many others). There are three facets that would theoretically use Merkle bushes: state, state transitions and arbitrary computations.
On the time of writing (August 2023) an opcode proposal (OP_CHECKCONTRACTVERIFY) has been formalized and carried out however earlier proposals included a number of completely different opcodes e.g. OP_CHECK{IN,OUT}CONTRACTVERIFY, OP_CHECK{INPUT,OUTPUT}COVENANTVERIFY, OP_PUSH_ANNEX_RECORD.
Extra data and a set of hyperlinks associated to those covenant proposals is right here.
