You actually just asked a question that has some the possibility for some very deep and intricate answers.

But we'll try to keep it simple. Disclaimer: the details have been dumbed down here for discussion/simplicity

First, let's get 2 quick defintions out of the way.

An "intersection" is a fix that is defined by an intersection of 2 identifiable courses, or 1 course and a DME.

A "waypoint" is a fix that is defined purely by lattitude/longitude points, and not crossing courses (used with GPS).

MERIT is an intersection defined by the following (per the LGA2.MERIT departure):

LGA R055, 49 DME

CMK R085, 21 DME

HTO R320, 46 DME

MAD R295, 21 DME

So legally you can intercept any of these radials, and when you cross another one of the radials, or cross the DME distance, you are at MERIT. As our good leader Jason described, the LGA2 departure says if you cannot proceed direct to MERIT, you'll be given a clearance to intercept the LGA radial.

I must admit this caught me off guard once. We have full RNAV capability, and our FMS doesn't mention anything about intercepting a radial, it just has us expecting a direct-to clearance. I was once given the intercept radial clearance and wasn't exactly ready for it. OOPS!