Learn Spanish (Latin America): Mis padres se abrazaron en el aeropuerto.

Here, se is a reciprocal pronoun that means "each other." While you might recognize se from reflexive verbs (where someone does an action to themselves), with plural subjects like mis padres, it often shows that multiple people are doing the action to one another. So, se abrazaron means "they hugged each other."

Could se abrazaron also mean "they hugged themselves"?

Grammatically, yes! Because se is used for both reflexive ("themselves") and reciprocal ("each other") actions, it could technically mean they hugged themselves. However, context usually makes it obvious. If you ever need to be perfectly clear that an action is reciprocal, you can add el uno al otro (each other) at the end of the sentence.

Why use the preterite abrazaron instead of the imperfect abrazaban?

The preterite abrazaron is used because the hug is seen as a completed, single event that happened when they met or said goodbye. If you were setting a background scene for a story (like "While my parents were hugging..."), you would use the imperfect abrazaban instead.

Why is en translated as "at" instead of "in"?