In brief: high energy, fairly diverse mix of tunes, speedy guitar work. Gordon Brown once said they wake you up in the morning; possibly (I haven't tried it), but they're great to listen to while you're working out; and fun in nightclubs too, of course, although I doubt Mr Brown knows much about that.
The lyrics: Alex Turner stands above Noel Gallagher, falls short of Jarvis Cocker and is miles below Morrissey (well, there's always somebody taller with more of a wit). The lyrics can be disjointed and incoherent but they do manage to raise a smile or two (On `Fake Tales of San Francisco' he sings, "I'd love to tell you all my problem/You're not from New York City, you're from Rotherham").
Other aspects of the songs are amateurish: the wimpy ending to `The View From the Afternoon', for example; on the same song there is an arbitrary pause halfway through which, needless to say, has no positive effect. The singing is technically not very good but having said that, Turner's broad northern accent - the `gritty realism', so called; the authenticity, the sincerity - is likeable, and on a song like `When the Sun Goes Down', actually quite moving. Technically, Whitney Houston has a great voice, but I'd rather stick needles in my ears than listen to an LP's worth of her tunes.
It doesn't matter that this album is not as polished as The Strokes' `Is This It' (the Arctics' biggest influence); and besides, Julian Casablancas spoils most of the songs by singing too close to the microphone. Someone should tell him it's not cool anymore.
The band is certainly not the new Smiths (the NME's hype machine in overdrive) - neither musically, nor lyrically nor in interview - but they are among the first to show that critical and commercial success can be found through the internet alone (with a bit of gigging thrown in). For the moment at least, the Arctic Monkeys are as super cool as their name suggests.