Compression reduces the peaks so you can raise the levels allowing you to hear the rest of the track better.
It will dull down the impact.
New york compression is a trick whereby you blend an uncompressed track with a copy that is heavily compressed.
That way you keep the initial impact (like the crack of the drum or the initial hit of the guitar) while also bringing up the subtleties of the rest of the sound.
Lots of compressors and other plugins have a blend function like the Prochannel compressors (wet/Dry) that does the same thing only easier.
The attack is about how soon you want the compressor to start compressing.
If you slow it down, more initial hit gets thru.