This is the 11018th most frequent Spanish word.
divorciar
To divorce.
In this sentence, 'divorciarse' is used reflexively to indicate that the subject is undergoing the process of divorce.
Mis padres decidieron divorciarse el año pasado.
My parents decided to get divorced last year.
Here, 'divorcio' is used as a noun derived from 'divorciar' indicating the legal process or situation.
El juez ejecutó el divorcio entre ambas partes.
The judge executed the divorce between both parties.
In this case, 'divorciar' is used transitively to signify the action of separating things.