Vertical scaling is adding oomph to the machine that an application is running on. Perhaps your e-commerce site is getting more traffic as your business grows, and it’s starting to creak at the seams. A common way to give the application a boost, is to add more RAM, more processors, more bandwidth, or more storage to your machine. Maybe you simply move your application to a new, more powerful machine.
Horizontal scaling, on the other hand, is adding more servers to your application to spread the load. The simplest case of horizontal scaling may be to move your database onto a separate machine from your web server. Now your web server can simply satisfy requests, and your database server can simply crunch data.