Hello, Helen. "Go to the mountain" means that you are going to one specific mountain "Go to the mountains" means that you are going to a place with a lot of mountains, like a mountain range. I will go to the mountain (Everest) I will go to the mountains (Himalayas)

'Go to the mountain' and 'go to the mountains' do not mean the same thing. The difference between the two is very small though. 'Go to the mountain' is telling you to go to that single mountain cause mountain is singular here. But when you add the s to say 'go to the mountains' you are now using the plural and telling them to go to multiple mountains.