Downloading, or just loading, generally refers to the acquisition of content (text, images, etc.) from a server by the browser. Unless you have a very slow connection, you can load more than one web page at a time into separate browser windows. Rather than just clicking on a link, right click (or hold the mouse down on the link if you're using a Mac) and select "open link in a new window" from the popup menu. This menu item may be slightly different in your browser (i.e., "Open Link in New Window").
A newer variation on this theme is tabbed browsing. Several modern browsers allow you to open links in tabs instead of new windows. The effect is the same, there is just much less clutter on the screen.
Then you can click back on the original page, read some more, or even open another link in a new window, while the other page is still being loaded. There is a practical limit to the number of windows )or tabs) you can have open at one time. Usually two or three windows will provide plenty of things to read about or look at while the other windows are downloading their content.