gradually; in sequence; in order
Expresses gradual change over time, meaning 'gradually' or 'little by little'.
次第に is a formal adverb that describes a process happening slowly over time. It is often used in written language, news reports, or formal speeches. In everyday conversation, you might hear it, but it sounds a bit stiff; casual alternatives like だんだん or 少しずつ are more common in speech.
When used with verbs, it indicates that an action or state progresses gradually. For example, 次第に良くなる (gradually gets better). It can also modify adjectives, as in 次第に寒くなる (gradually gets colder).
Note that 次第に is different from 次第で, which means 'depending on'. Don't confuse them.