I understand the meaning of the component words, but what does the phrase mean and how is it used? From an internet search it seems to mean something akin to we will find our reward in heaven.
It's about expectations of changes for the better, of hopes to succeed in foreseeable future, most likely ungrounded hopes.
It was popularized in Chekhov's "Uncle Vanya", one of the most famous plays in the world. Actually most likely it was invented by Chekhov, though this should be verified, that's why I'm carefully using "popularized"
Here's exact quote:
Мы отдохнем! Мы услышим ангелов, мы увидим все небо в алмазах, мы увидим, как все зло земное, все наши страдания потонут в милосердии, которое наполнит собою весь мир, и наша жизнь станет тихою, нежною, сладкою, как ласка.
Just like it happens quite often with other pathetic and romantic phrases it was later ironically rethought. For instance:
"Я думал, русские женщина горячие", - беспардонно заявил он, придымливая шестую сигару.
"Я те устрою небо в алмазах", - злобно пообещала Марина.
But keep in mind that though this phrase is most likely known by native speaker, it's usage quite limited.