Learn Hardcore Russian: Лампа горит ярко, когда я читаю книгу ночью. - The lamp shines brightly when I read a book at night.

The verb горит comes from гореть, literally “to burn.” When you say Лампа горит, you mean “the lamp is lit” or “the lamp’s bulb is on.”
By contrast, светить means “to shine” or “to give off light.” Both are possible with лампа:
• Лампа горит focuses on the lamp being switched on (the filament burning).
• Лампа светит highlights the act of emitting light.
Native speakers often use гореть for lamps, candles, fires, etc., and светить for any object that radiates light.

Why is ярко used here, and how is it formed?

Ярко is an adverb meaning “brightly.” It’s formed from the adjective яркий (“bright”) by replacing -ий with the adverbial suffix -о.
Position-wise, Russian adverbs of manner usually follow the verb: горит ярко. You could also say ярко горит, but the first version is more neutral.

Why is книгу in the accusative case?

The verb читать (“to read”) requires a direct object in the accusative case.
• Книга is nominative (the subject).
• Книгу is accusative (the thing you’re reading).
So я читаю книгу = “I am reading a book.”