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." The word then came to be used figuratively, as when your parents impress upon you the importance of being honest or when you impress the judges at a diving competition. Impress can also mean to conscript someone into the army.