The Mirriam-Webster definition of this is “to recite the perscribed prayers in a Jewish liturgy.”
Related word: Shuckeling
This refers to the swaying motion that Jews perform when they are davenning. Both words have their origin in the Yiddish language.
The Jewish liturgy has different sections which must be prayed at specific times throughout the day, so davenning is an integral part of every religious Jew’s every-day life.