A quad equalizer is an audio tool with four separate filters, each one boosting or cutting a different range of frequencies in a sound.
"Quad" means four — in this case, four bands: low, low-mid, high-mid, and high. "Equalizer" comes from the original engineering goal of "equalizing" uneven frequency response in early audio systems; today the term covers any tool that reshapes a sound's frequency balance, whether to fix a problem or just to suit personal taste.
It's not a volume control (though this tool includes one separately), not a noise remover, and not a way to separate vocals from instruments — a quad equalizer only reshapes the balance between frequencies that are already present in the audio.
Curious about the mechanics behind it? See How Does a Quad Equalizer Work? for a closer look at the filters involved.