In earnest

What does it mean when someone says, "began in earnest?"

It means that it began with seriousness or sincerity.

We may need more context. When a person begins to speak in earnest, for example, the meaning is as above. "As the storm approached, the wind began to blow in earnest" means the wind became more forceful. If what began in earnest was a construction project, the meaning would be yet again a little different. ~rb