Once upon a terribly long time ago there was a Latin word exprimere, which meant to press out, and the past participle of which was expressus. When you press your seal* into soft wax you produce an image, and, so far as anybody can tell, that's why the Latin word took on the meaning of describing or representing something.
Cows expressed milk, sores expressed pus and human beings were expressed by God. Very quickly people got the idea of expressing thoughts as words, as though the mouth were the udder of the mind. Thus Chaucer's:
Thy virtue and thy great humility
There may no tongue express
Also from this came the idea of something that was specifically, or expressly, designed for one purpose and for no other. If God expressed man, he did it rather well, or at least that's what Hamlet thought:
What a piece of work is a man! how noble in reason! how infinite in faculty! in form and moving how express and admirable! in action how like an angel! in apprehension how like a god!
We still use this meaning when we say expressly. Thus today's Guardian:
In a work expressly intended for students to perform, Pountney has created a dramatic structure that interlocks three stories of 20th-century student political action...
So how do you send a letter? Do you entrust your epistle to the general mail, or do you employ somebody expressly to deliver it? Do you find a chap, give him one letter and express instructions? If so, then you have sent the letter express.
The same sort of thing happened to trains. Some trains dawdle. They may say on the front that they are going to Euston, but once aboard you discover that they are in no great hurry to get there and that you will probably be pausing at Moreton-St-Davids for an hour or so while they load up the baggage car with sheep. What you need is a train that is meant expressly and exclusively for Euston, a train that does not stop anywhere else.
These days express trains aren't very express and will probably terminate at Preston on a whim, but that's not how it once was, dear reader.
And so a word that meant press out came to mean describe and intentional and specific and fast and non-stop.
And espressos? Though an espresso should be drunk quickly and is probably expressive of something or other, the dwarf coffee owes its name to the original Latin. You see, the steam is pressed out through the coffee grains and into the bonsai cup.
Like a cow expressing milk
*By which I mean a coat of arms, not a marine mammal. I made that mistake once and the zookeeper got cross.