[imjoshholloway]

Vertical scaling is where you add more resources to a machine. E.g; more RAM or processing power.

Horizontal scaling is where you add more machines to your pool of resources (servers).

Examples;

Horizontal scaling would be adding more web servers behind the load balancer to facilitate more traffic.

Vertical scaling would be adding more RAM to your database server to keep all the data (or just the indexes if your database is that big) in memory.