A subpoena duces tecum for deposition is a subpoena which commands a person to appear before a court or other tribunal and to bring specified documents, records, and other listed items with him/her, for the purpose of a deposition (out-of-court testimony reduced to writing for later use in court or for discovery purposes).
The subpoena duces tecum for deposition "in aid execution" is a subpoena which, again, commands a person to appear with specified items for a deposition, this time to aid in the execution of a judgment. It's purpose is basically to discover any assets upon which an execution of a judgment may be made. In other words, "in aid executions" are depositions done post judgment, or after a judgment has been made. Execution is the act of carrying out or putting into effect (as in a court order), and this post-judgment deposition will "aid" in that act.
The law allows for post-judgment discovery or depositions to discover what assets not revealed before in a pre-judgment deposition may be available to attach in order to satisfy the judgment.
In a debtor-creditor situation, for instance, discovery done prior to the hearing may not have revealed all assets (perhaps all that was asked for was income and checking and savings amounts). If a debtor is awarded a judgment against the creditor, and the creditor, say, is unemployed or has a low income, the debtor may want to see if he can get the judgment satisfied by forcing the sale of some of the creditor's other assets (a car or jewelry or whatever). This post-judgment deposition would provide the debtor with the chance to discover any hidden or heretofore unrevealed assets.
(If I got any of this wrong, someone will be along shortly to correct it.)