Why are babies so into stairs climbing or anywhere they see people can go up and down?

Agree with Nooraini! They operate on a i-see-therefore-i-do basis because at that age, their minds and bodies are developing and everything seems new and utterly fascinating to them. Stairs and staircases are excellent ways for them to explore and try out new things -- visually and mentally, the idea of going up and down surfaces excites them. Best to supervise and make sure they don't hurt themselves though.