Parallel or ‘New York’ compression is simply the concept of splitting a signal at source into two parallel paths, compressing one while leaving the other unscathed. Once you blend the two back together, you should, in theory, be combining the benefits of compression while retaining the air and cleanliness of the source.
However, in truth, the technique tends to be used to take advantage of the colour a compressor can add, so in many cases you’ll be pushing the compressor harder and then blending the unprocessed signal back in with that. You’ll typically see it used for processing transient heavy sounds such as kicks and snares, and also for fattening up lacklustre vocals. Get it right and the results will differ from simply using the compressor on its own. But it can be a fiddly technique, and it’s very dependent on the level balance between the two signals.
There are two ways to approach it: one is the old-school method, originally developed on analogue desks where you would split (or ‘mult’ to use the US terminology) the source down two desk channels. On one channel you can then insert your desired compressor, setting it to compress hard, bringing up the tail of sounds and generally fattening them up. On the second channel you can then blend back in the raw source, regaining some of the lost transients or in the case of a vocal, articulations. So far so good. But the technique can then be further finessed by EQing each channel slightly differently. In a DAW environment, one can use linear phase EQs to minimise phase smear between the two channels.
The second way to approach parallel compression is to use a compressor with a mix blend (dry/ wet) control. This is much quicker and can also give you an idea of whether the technique is worth a try. However, you clearly miss out on the additional EQing option, and achieving an accurate balance using a ‘mix blend’ is arguably much harder than blending two fader levels.