If you run into that cute guy (or girl) from the local deli when you’re at the grocery store and you stop to chat, you’ve just had an encounter, which is a casual meeting, often resulting by chance.
When you encounter the word encounter, context will tell you if it’s acting as a verb or a noun. The sentence “When Spencer and Susanna encounter a bear on the trail, they stand very still” illustrates the verb form. “The encounter in the subway left her wishing she had stayed at home” shows the noun form. Whether acting as a verb or a noun, the word carries the connotation of “chance meeting." You don’t plan an encounter; it just happens.