The word latían is the imperfect form of latir in the third person plural.
See the full latir conjugation

latir

Con sus sueños de una nueva alborada latían vivas expresiones de arte y música.
Lively expressions of art and music pulsed with their dreams of a new dawn.
Todos los corazones latían armoniosamente.
All hearts beat in harmony.
La fiesta finalizó con un coro extraordinario, y los corazones latían de esperanza y alegría por el futuro que nos espera si vivimos una vida victoriosa sobre el pecado.
The feast ended with a riveting choir piece. Our hearts beat with hope and joy for the future that is awaiting us if we live an overcoming life.
Que latían por mí.
It was beating for me.
Mientras nuestros corazones latían fuerte y el sudor escurría por nuestras caras, mi residente y yo nos sentamos en la estación de enfermeras a respirar y reagruparnos.
Our hearts pounding, sweat running down our faces, my resident and I sat down at the nurses' station to breathe and regroup.
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