A date is a particular day of the month, and to date is to go out with someone. You might have the date of your first date with a special someone marked on your calendar. Awwwwwwww.
Date comes from the Latin datus, "given," because in ancient Rome when people wrote letters or decrees, they'd say, "given ("data") May 1st" (for example). Date can mean a day of each year, like May 1st, or one historical day, like May 1st, 1873. You make a date to meet someone for dinner. You date your letter. If you make many appointments with one special lady, you're dating her. A date is also a fruit, from the date palm.