Think of the verb impress as "leaving a mark." You might impress a print onto canvas, or you might impress prospective employers in a job interview. Whether that impression will be good or bad is up to you!
The past participle of the Latin verb imprimere, "to press," is impressus, which evolved in the 14th Century to the meaning "to make a permanent image." That meaning included a figurative meaning of "to impress upon the mind or heart." Impress also means conscription into the military, or taking people to serve against their will — in other words, the draft.