you can think of a non-fungible token as basically a certificate of authenticity that can verify the ownership of a digital thing. for example, if you take a photo and upload it to facebook, any number of people can download/save the photo, and there is no real way for anyone to verify who has the ORIGINAL photo. if you "mint" the photo as an NFT, that photo now has a credential attached to it to verify it's status as THE original photo. this can be applied to ANY kind of digital asset, not just photos.
bitcoin and other cryptocurrency "mining" is basically a term for using a computer (or several) that you own to contribute brainpower to the global network that does calculations to verify transactions of cryptocurrencies. you get paid a little bit in exchange for contributing this computing power to the network.