Audio interface/soundcard
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A device that gets audio in and out of your computer. All computers and laptops will have a basic built in sound card that will handle inputs (mic/line in) and outputs (to speakers/headphones). For professional audio you will need an additional soundcard/interface. These comes in various forms, USB, Firewire and PCI devices.
Understanding recording hardware
For a comprehensive list of known supported hardware, check out this AV Linux forums thread.