The figure of speech (also called poetic device or literary device) in the following line of Shakespeare's "Sonnet 116" is personification.
Let me not to the marriage of true minds.
Personification is the giving of non-human/non-living things the ability or characteristics seen in humans. For example, "the clouds cry". Clouds are objects. In the example, clouds are stated to cry. Crying is a human ability and clouds cannot literally cry. The clouds are given a human ability (crying) and this is personification.
The personification in this line comes from the understanding of the word "marriage." If one looks at the action of marriage, and not the process of marrying (joining two things such as oil and water together), one could justify that marriage is a ceremony which only two people can take part in. Minds cannot be married, only people can.
Another figure of speech that could be justified in the line of poetry is a hyperbole. A hyperbole is an exaggeration which an author uses with the intent that it not be taken literally, but importance lines in the meaning or symbolism of the hyperbole used. Here, the marriage of true minds could be justified as a hyperbole given minds cannot marry. Regardless of the fact that minds cannot marry, readers understand that the symbolism of the image is of much more importance- two minds being brought together with "true" thoughts.
With either example or explanation, remember that poetry is subjective. This means that the meaning or interpretation of a poem, or line of poetry, is left up to the feelings which the poem brings out in the individual reading it.