This is the 7672nd most frequent Russian word.
зайцев
"Зайцев" is the plural form of "заяц," meaning "hares" in English.
In this sentence, 'зайцев' is the genitive plural form of 'заяц', the word for 'hare', used here to mean there were many hares.
Я видел много зайцев в лесу во время прогулки.
I saw many hares in the forest during the walk.
Here, 'зайцев' is the genitive plural form that contextualizes the focus of the hunting – the hares.
Книга рассказывает о приключениях охотника на зайцев.
The book tells about the adventures of a hunter for hares.
In this case, 'Зайцев' serves as a plural surname indicating a family named 'Zaytsev' that the speaker intends to meet or discuss with.