Indicates that two or more actions are happening at the same time.
Example
노래를하며공부를한다.
I study while singing.
빨갛고매운음식을먹으며스트레스를푸는장면을본적이있나요?
Have you ever seen a scene where you de-stress by eating red and spicy food?
2.
Listing actions, states or facts
Used to list two or more actions, states, or facts. Mainly used in written language or formal situations.
Example
그곳은마치고향처럼아늑하고포근하며정겨운느낌을주는곳이다.
That place is cozy, warm, and give a feeling like home.
한국사람들은매운음식을좋아하며일을빨리처리한다고들었다.
I heard that Koreans like spicy food and get things done quickly.
3.
Listing things
When used with 이다, it used to list two or more things or statement. Also implies that they are large in number and there are more than just the listed items.
Example
돈이며명예며관심없다.
I don't care about money or fame.
무며오이며부추며갖가지채소로김치를담근다.
Kimchi is made from various vegetables such as white radishes, cucumbers, and leeks.