Well, there is no short or clear answer! In traditional Italian coffee an espresso roast would be a very dark and oily roast that probably contains a percentage of robusta (a cheaper more bitter coffee variety). By roasting dark and using robusta they were able to create a coffee that isn't too picky about grind, doesn't significantly change taste as it ages and creates a lot of crema (the light brown foam on an espresso shot).
We at Other Brother Roasters like to keep it simple - an espresso roast is anything you would put into your espresso machine. Any coffee can be a used to make espresso but there is one thing especially that makes espresso easier to work with and that is solubility. Roasting a coffee to be brewed in a drip coffee maker (which takes a few minutes) is different than roasting for espresso (which takes a few seconds to brew) because we want the coffee to extract at different rates. So through some tricks of roasting we are able to increase the solubility of a roasted coffee (even at a light roast) so that it extracts nicely and evenly when brewed as espresso. Another thing we do when roasting for espresso is tame the acidity (or liveliness) because the espresso brewing method tends to accentuate this more than other brewing methods.