Urgente vs. apremiante

In the Spanish language, 'urgente' and 'apremiante' might both translate to 'urgent' in English, but they are not used interchangeably. The difference resides mainly in their contextual and idiomatic usage, and a slight nuance in sense of urgency conveyed.

Urgente

'Urgente' directly translates to 'urgent' in English. It's commonly used to describe situations, needs or issues that require immediate attention or action.
Es urgente que terminemos este proyecto.
(It is urgent that we finish this project.)
Llámame, es urgente.
(Call me, it's urgent.)

Apremiante

'Apremiante', also translating to ‘urgent’ in English, often conveys a sense of pressing or overwhelming urgency. It is used less frequently than 'urgente' and commonly pertains to issues that not only need immediate attention but also imposes remarkable stress or pressure.
La pobreza es un problema apremiante en esta región.
(Poverty is a pressing issue in this region.)
Tengo una necesidad apremiante de hablar contigo.
(I have an overwhelming need to talk to you.)

Summary

In summary, while both 'urgente' and 'apremiante' translate as 'urgent', 'urgente' generally implies an essential or important objective that requires quick attention or solution, whereas 'apremiante' leans more towards an urgent matter that exerts considerable stress or demands immediate and drastic action.