In the US, a geezer is an old man--preferably one who looks something like the picture on the left.
In informal British English, however, geezer means something more like dude means in AmE. (But unlike dude, people don't go around addressing each other as geezer.) It can be used for any man, or to connote that someone is 'one of the lads' (US: guys) or a bit cheeky or laddish--i.e. a bit naughty. A diamond geezer is a great guy. A dodgy geezer is someone you're better off avoiding. Geezer used in this way has a bit of east London attitude to it.
One sometimes sees babygros (UK)/onesies (US) emblazoned with GEEZER, as in the picture on the right. Thought about getting some of these for my infant nephews, but thought they'd only cause consternation in the US.