Translation:Your grandmothers and grandfathers love you.
себя would mean "yourself" here but you can see that doesn't make sense in English.
Себя does not mean “yourself” here. Себя will refer/reflect to the subject (nominative) of the sentence. The subject of the sentence is бабушки и дедушки. The subject is not твои, which is just a possessive adjective.
“Твои бабушки и дедушки любят себя” would mean they love themselves. [A native Russian speaker will have to weigh in on whether there are shades of, “they only love themselves, not even each other,” which is how I would automatically read such a Russian statement. I would expect that love for one another to be expressed using “любят друг-друга.”]