Late Middle English: from Old French compresser or late Latin compressare, frequentative of Latin comprimere, from com- ‘together’ + premere ‘to press’; or directly from compress- ‘pressed together’, from the verb comprimere.
In the sense ‘to convey in words or by behaviour’, express originally meant ‘to press out, obtain by squeezing’, and its root is Latin pressare ‘to press’. Express meaning ‘intended for a particular purpose’ is from another Latin word meaning ‘to press’, primere, and is the source of express train and other uses that involve high speed. As early as 1845 an express train went ‘expressly’ or specifically to one particular place, not stopping at intermediate stations. This would have been a relatively fast train, and led to the word being interpreted as meaning ‘fast, rapid’.
Late Middle English (in the sense ‘apply with pressure’): from Old French empresser, from em- ‘in’ + presser ‘to press’, influenced by Latin imprimere (see imprint); sense 1 of the verb dates from the mid 18th century.
The words press and print ultimately come from the Proto-Indo-European root per– (sense 4) meaning “to strike,” an extended sense from the same root (sense 1) meaning “forward, through.“ The root (sense 4) is also the source of pregnant (in the sense “full of a quality or feeling“), reprimand, and imprimatur—beware of the spelling of these words as they do not resemble the stems. Also beware of the following words: empress, lypress, pressie—they may look like the base, but they do not come from the same root.