Descansar vs. reposar

Both 'descansar' and 'reposar' are Spanish verbs that translate to 'to rest' in English. However, they are not always interchangeable as they may convey slightly different implications depending on the context.

Descansar

Descansar primarily relates to rest following physical activity, work or fatigue. It can mean to take a break, to sleep, or to have a day off.
Voy a descansar un rato después de correr.
(I'm going to rest for a while after running.)
Él ha trabajado mucho esta semana y necesita descansar.
(He has worked a lot this week and needs to rest.)
Los domingos son para descansar.
(Sundays are for rest.)

Reposar

'Reposar' often refers more specifically to resting in order to recuperate health or strength, or letting something else rest for better quality. That something could be food, drink, or an art creation, etc.
Después de la cirugía, el doctor le dijo que reposara durante una semana.
(After the surgery, the doctor told him to rest for a week.)
Deje reposar la masa antes de hornearla.
(Let the dough rest before baking it.)
Es mejor dejar reposar el vino antes de beberlo.
(It is better to let the wine rest before drinking it.)

Summary

'Descansar' and 'reposar' both translate into 'to rest', but the former is more general and commonly used for resting after activity/work/fatigue or taking time off; whereas 'reposar' is often used more specifically for resting to recuperate one's health/strength or allowing food/drink/artworks/etc. to sit and develop better quality.