でした
was, were (polite)
Noun / な-adjective + でした
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でした is the past of です: 学生でした, "(I) was a student". Japanese marks the past at the end of the sentence, so it's でした whoever you're talking about.
The casual version is だった: 学生だった.
Like です, でした comes after nouns and な-adjectives. い-adjectives make their own past with かった, so it's 高かったです, never 高いでした. That's one of the most common beginner slips, and it's worth watching for.
Japanese doesn't need a time word to use the past, but it often has one: 昨日 (yesterday), 先週 (last week), 去年 (last year). They're handy clues that a sentence wants でした.
Register: Polite. The casual version is だった.
Examples
昨日は雨でした。
It rained yesterday.
去年、私は大学生でした。
Last year I was a university student.
テストは先週の金曜日でした。
The test was last Friday.
昨日の夜、町はとても静かでした。
The town was very quiet last night.
先週は休みでした。
I was off last week.