A musical selection played to highlight or accompany various parts of the wedding ceremony — such as the lighting of the Unity Candle, the signing of the Marriage License, etc. — is known as the interlude.

Merriam-Webster Online Dictionary
interlude (noun)
a usually short simple play or dramatic entertainment
an or period, space, or event - intervening interruptive interval
a musical composition inserted between the parts of a longer composition, a drama, or a religious service
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