We use "would like" to describe our wishes, plans in the future etc. For example: I would like to go to the cinema. I would like to visit my grandma. They would like to learn a foreign language. Something like that. :)

It's used to politely express interest in ____ "I would like to join the drama club" - I want to join the drama club "Would you like to join me for lunch?" - Do you want to come to lunch with me?