Yes, it is a bit confusing to see "Download" and then be taken to a page of code. But anyhow, as Allan says, you can just click File > Save As, or whatever you see at the top left of your screen. Or you can copy all tat code and paste it into a file of any name you choose, such as jquery.js.
There are two ways to link to jQeury: by storing a file on your server, such as
or you can link directly to an online version of jQuery, such as
Either way, make sure to put the link to the jQuery script before/above links to any other jQuery code on your page. Otherwise you'll get errors.
Lastly, be careful not to make all your links only relative to folders on your computer. Paths like /Users/Am/Desktop/Swift.Files/ are going to fail once you pt your code online. If you are using server-side code like PHP, then set up a dev environment on your machine to mirror the online setup, so that your code will work in both places. You can download something like MAMP or XAMPP for that purpose.