Meta (/ˈmɛtə/; noun): (of a work) referring to itself or to the conventions of its genre; self-referential.
Referring to transactions this would mean, a transaction meant to transact a transaction (!). Put differently, the original user (the one who wants to transact) passes on their intent to perform a transaction on the blockchain. Another user, picks it up and performs the transaction on behalf of the original user.
User Alice -> Signs on a function doSomething(params) (Note, the user signs on the function not a transaction) -> sigOfAliceToDoSomething. Alice here generates a signatured intent to perform the action. Some other user, say, Bob, takes the signature sigOfAliceToDoSomething -> unpacks it to verify Alice as the sender -> gets to the intent doSomething(params) -> performs the action (Note, the action doer here is Bob and not Alice) -> and does whatever it is to be done with the returned values.
Now, this entire architecture is vague and has a lot of areas that can be separately dealt with. Some of which are listed below:
Now there might be multiple ways this problem statement can be formulated in, to focus on a particular aspect, or tackle a much bigger problem - and there in fact exist some, e.g., (chronologically arranged)