Musically speaking:
Punk is defined by a few things - the most noticeable being the tempo. Most punk music is above 130bpm (however there are always exceptions).
Hence punk songs are short. They follow pop structure, but due to the tempo, will finish quicker. (short doesn't necessarily mean 'less', as structurally, punk music is just as full as any other style).
Harmony - generally simple. Basic chords. Usually just power chords on the guitar. This is also to do with the tempo. The faster something is, the less complex it needs to be, as the speed keeps the interest as much as/if not more so than the actual harmony itself. Most punk songs will only have a few chords, as this is all that's needed at a high tempo.
Instrumentation - as for rock.
Vocals - generally rebellious/anarchistic (with lots of swearing!). The vocals can be shouted as much as they are sung, and originally in punk were shouted more, as this was more effective for translating the anger/annoyance of the lyrics than actually singing about it.
There are a few more things, but the things stated are traditionally the idiosyncrasies of punk.
Modern bands such as Green Day/Blink/MCR etc wouldn't be considered 'pure' punk, as vocally they are too melodic. Hence they get the 'pop punk' label. Everything about their music is punk, apart from the vocals being very melodic i.e. 'singable'. Hence those bands are the ones who have broke through into the mainstream, as they treat the vocals as they would be treated in writing a pop song i.e. very melodic.
Hope that helps a little.