This is a common, slightly poetic way to announce the arrival of the season. What makes Japanese feel so different from English is that words don't carry their grammatical role through position — they carry it through small tags called particles that come right after each word. You could swap the order of 里に and 春が and the sentence would still make sense, because each phrase is labelled.
The sentence has a backbone. The subject and the verb sit together on one horizontal line, divided by a vertical line that marks where the subject half ends and the predicate half begins. Anything that adds detail — here, the location — is stacked above the phrase it belongs to.
Read the diagram from the bottom up: 来ました is the core that everything resolves into, 春が is what the sentence is about, and 里に rides above the subject as supporting detail.
Five pieces, each doing one job. Read them in order and the sentence assembles itself.
里 means "village" or "countryside" — a word with a soft, nostalgic feel.
The particle に tags the word before it as a location or destination, so 里に means roughly "to the village." It is the closest equivalent to an English preposition — except it comes after the noun rather than before.
春 means "spring" — the season, and the thing performing the action of the sentence.
The particle が marks the word before it as the subject. So 春が tells you spring is what is doing the coming. が specifically introduces new information, which fits a sentence announcing a fresh seasonal change.
The verb, and in Japanese the verb almost always comes last — the sentence gathers its pieces and then resolves with the action. It is built from two parts: the verb 来る (kuru, "to come") and the ending ました, which makes it both polite and past tense.
Read in its original order, the sentence is literally a chain of labelled pieces that an English translation then re-arranges.