To combine clauses or adjectives, as if by the English conjunction "and". For example:
薬局へ行って薬を買う yakkyoku e itte, kusuri o kau: "(I am going to) go to the pharmacy and buy medicine."
あの人は親切で頭が良くて分かり易い ano hito wa shinsetsu de, atama ga yokute, wakariyasui: "That person is kind, smart, and easy to understand."
安くていいね yasukute ii ne: "It's good that it's cheap." (lit. "Being cheap, it is good."