What is a gated category on Amazon?
Categories and brands you need Amazon's approval to sell in.
Some categories, brands and individual products are "gated": Amazon requires approval before you may sell them. Grocery, topicals and certain toys are commonly restricted; many brands gate themselves to fight counterfeits. A new account has more gates than an established one.
For arbitrage the rule is simple: check eligibility before you pay, not after the box arrives. A deal you cannot list is not a deal. Eligibility checks are built into scan results for exactly this reason, and requests to sell ("ungating") often just need an invoice from an authorised supplier.