A matter synthesizer was a technology in use in the Federation during the 23rd century, which worked through matter synthesis.
Much like the later replicators, they were used to create certain day-to-day necessities for life aboard starships, specifically food and uniforms. Food specifically was dispensed from food synthesizers. (DIS: "Context Is for Kings", "The Butcher's Knife Cares Not for the Lamb's Cry")
When Sylvia Tilly was nine, she worked out how to make her matter synthesizer produce only spumoni ice cream by calculating the exact protein concentration and small particle dispersion of emulsifiers required. (ST: "Runaway")
Although I AM ERROR depicts the technology very similar to how replicators were depicted, the technology was presumably not the same, since a line from VOY: "Flashback" established that replicators did not yet exist.