Definition of this sentence "your dark eyes encounter me

Supposing you want to identify the figure of speech in this sentence, it is synecdoche. We use it when we want to refer to a part of something to signify the whole of it. In this case, the speaker refers to the dark eyes instead of the whole person who encountered them. The scene and the interaction probably have to do with love, as people who are in love are often enchanted with their beloveds' eyes.