Website hosting is [basically] the location of the files for your website. There are many types of hosting, but for most music teachers, the simplest and most affordable will suffice.
For a self hosted WordPress website, I recommend the hosting at SiteGround.
Buy as many years or months as you feel comfortable purchasing. This will keep the cost down for you over the long term.
If you want to go the DIY route, Squarespace is a very solid option. Avoid Wix and GoDaddy’s page builders.