A video that is very "in demand" will distributed it to data centers and "peers" across the world. Peers meaning YouTube/Google makes agreements with ISPs to host popular videos on their servers which are as close as possible the end users, this applies to pretty much all big streaming services.

Streaming doesn't require the server to send the whole video at once, it only needs to send a steady stream of little chunks of the video to each individual viewer every so often.