Whats the purpose of the box in Proteus?
"The blue box" is the outline of the chosen page size. (See step 2 of that tutorial.)

Blue box:


When you start a new design, you can select from various templates.  Each template includes a page size.

If you were to print (or plot) your design, then everything in the blue box would be printed on a sheet of paper the same size as the blue box.

If you start from an A4 template, and keep everything in your design inside the blue box, then you can print it out on standard european letter size paper and your whole design will fit on one page.

If you start from an A0 template, then you will need a very large printer (or a plotter) to print your design on a single page.