When you elope, you run away with the person you love. Usually, you elope to get married without anyone knowing in advance.
The word elope probably originated with the Middle Dutch word lopen, meaning "run away." Couples who elope typically don't seek anyone's permission before running off to get married, not even their parents. Often, that's the whole point of wanting to elope: you can avoid dealing with anyone who might opt to "speak now" instead "holding their peace."