To leap at or jump onto something; to pounce on. Also used figuratively to mean eagerly seize an opportunity or accept an offer immediately.
犬が餌に飛びついて食べ始めた。
The dog leapt at the food and started eating.
彼は安売りの話を聞いてすぐに飛びついた。
He immediately jumped at the deal when he heard about the sale.
危なかったので手すりに飛びついて体を支えた。
It was dangerous, so I grabbed the handrail to steady myself.