Learn Spanish (Latin America): Llovía cuando se besaron.

In this sentence, se acts as a reciprocal pronoun meaning "each other." The verb besar means "to kiss," so se besaron means "they kissed each other." Without se, it would just mean they kissed someone else!

Why does this sentence mix the imperfect tense (llovía) with the preterite tense (besaron)?

This is a classic way to tell a story in the past! The imperfect tense (llovía) sets the background scene ("it was raining"), while the preterite tense (besaron) is the specific, completed action that happened in the middle of that scene ("they kissed").

Where is the word for "it" in llovía ("it was raining")?

Spanish doesn't use a subject pronoun like "it" for weather. The verb llover (to rain) just conjugates directly to the "he/she/it" form. So, llovía all by itself means "it was raining."