Learn Russian: Именно осенями медведи ищут пищу, готовясь к спячке. - Precisely in autumns, bears look for food, preparing for hibernation.

This is the instrumental of temporal iteration. When a season like осень is used in the bare instrumental plural, it means the action happens repeatedly during that season over multiple years. Here, осенями translates to "in the autumns" or "every autumn."

What is the purpose of Именно at the start of the sentence?

Именно means "precisely" or "specifically." It acts as an emphatic particle that highlights the word immediately following it. In this sentence, именно осенями stresses that this intense search for food happens specifically during the autumns, rather than any other time of year.

What verb form is готовясь?

Готовясь is an imperfective verbal adverb (sometimes called a gerund) meaning "preparing." It indicates a background action happening at the exact same time as the main verb (ищут), performed by the same subject (медведи).

Why does "preparing for hibernation" use к спячке instead of a word like для?

The reflexive verb готовиться (to prepare oneself) requires the preposition к followed by the dative case to indicate what you are getting ready for. Therefore, "to prepare for hibernation" must be expressed as готовиться к спячке.