Converters take your sound and convert it to digital so you can record it digitally on your computer.
What are converters?
Digital Audio Converters, DACs, or Converters do just that; convert audio from analog to digital and back again. Therefore you will often see them referred to as A/D/A, or analog-to-digital-back-to-analog.
In practice converters are usually contained within audio interfaces, although its almost as common to see them as stand-alone units (generally rack units or PCI cards with or without a breakout box).
When talking about converters, its a common shorthand to use them simply to refer to the A/D part - taking your analog signal and converting it to digital before transmitting via lightpipe, ADAT, Firewire, USB or other digital cable to your DAW. This refers to our basic signal chain:
Mic > Preamp > A/D > DAW
However the D/A part is just as important, turning the sound back to analog simply so it can reach your speakers in the most common setups. More complex applications will involve more D/A converters to create other output channels for submixes, headphone mixes, or sending audio back from the recording in the DAW to outboard gear such as an analog summing mixer.
Generally one refers to converters by the number of channels they have i.e. a 10/10 has 10 input A/Ds, and 10 output D/As.
Common terms when referring to converters
In theory, a converter should be a transparent part of your signal chain as all it is doing is calculations. You will see lots of theorizing and soap-boxing based on the fact that the mathematical calculations are the same from unit to unit.
In fact, as there is no such thing as a perfect system, there is an easily audible difference between, as ever, cheap and pro converters.
Nonetheless, most of the terms referred to in distinguishing types of converters are generally within the mathematical scope and give little to no idea as to how they perform in reality. As ever, nothing below $500 is going to be capable of giving you the best results, with some excellent value models right up to the higher stages of pro occurring between $500 and $3000 after which diminishing returns will set in.
Sample rate - your DAC will have a choice of sample rates to operate at
Bit depth - the conversion will generally occur at the highest bit depth the converter can offer - generally 24-bit
Latency - when monitoring the signal zero-latency monitoring will refer to a direct feed from the inputs, the latency itself refers to the delay caused by conversion time
Phantom Power & Preamps - many converters will offer a few preamps and therefore phantom power to go with them. This increases utility and quality is as variable as ever
Transformer-Coupling - will often be offered on inputs and outputs
Variable Line Levels - most units will be configurable to work at -10dBu, +4dBu, or more nominal line levels
Clocking - the device by its nature will have an internal clock, dependent on the quality of this it may offer to act as a master clock for your system
Inputs and Outputs - again by its nature your converters will receive multiple signals inwards and outwards. The bulk of the analog audio will enter and leave by TRS jacks most commonly, with ADAT ins and outs being a good way of offering additional sets of 8 I/O without taking up too much chassis space. SP/DIF, coax, and other input/output formats will often be offered to expand inter-connectivity.