Learn Russian: У них большое горе.

When talking about abstract concepts, emotions, or illnesses in Russian, the word есть (to have/to be) is typically omitted. This is especially true when the noun is modified by an adjective. The focus is on the intensity of the feeling (the great sorrow) rather than the mere fact of possessing it.

Why use большое (big) to mean "great"?

Russian frequently uses the adjective большой (big) with abstract nouns to express intensity, depth, or a high degree of something. You have probably seen this before in the phrase большое спасибо (thank you very much). Here, большое горе naturally translates to "great sorrow" or "deep grief."

What gender is the word горе?

It is a neuter noun, which you can tell by its -е ending. Because it is neuter, the adjective modifying it must also be in the neuter form, which is why we see the ending -ое in большое.

Is горе used for everyday sadness, or only for serious tragedies?

Горе is a very strong word reserved for deep grief, profound sorrow, or a major tragedy, such as a death in the family. For everyday sadness or minor upsets, you would use a word like грусть (sadness) or печаль (sorrow).