It's important because it activates online monitoring.
In general, the ISRC code allows you to uniquely identify your track; so you need to add it to each of your tracks and to every version you may have.
You can do this as the first or last step of the registration procedure or later on using
the Actions > Versions/ISRC tool.
In Italy, the only national agency appointed by IFPI is FIMI, from whom you can request a code by filling in the form on their website.
Don't forget that ISRC codes are also issued by digital distribution services.