Horizontal Scaling :
To resolve the above problems(high cost/hardware limit) instead of putting all the resource into one machine, we are putting multiple machine with normal resources, so that we can handle any amount of request without worrying of hardware limitation. When traffic grows we can simply add more servers(& vice versa) and the website will run smoothly. We can simply achieve this using "autoscaling" feature on AWS.
But the catch with vertical scaling is, we need to implement load balancer which can distribute the traffic equally among all the machines and have to make our web servers(machines) stateless to able to provide responses to user from any machine irrespective of what machine it was logged in first.
What do I mean by stateless ?
If you have build any web application with some authentication or used cookies for storing particular information about the user for a constant time. Typically when you using a cookies for a particular session(user), these details reside with in that machine only. So let's say if a user performs logging in ServerA but due to huge request load balancer redirects the same user to another ServerB after login succed. But this ServerB doesn't have any knowledge about the session created in ServerA. So then ServerB again asks user to login. If you have 'n' machines then in worst case the user have to login in every machine(n) to use the application which is very bad User experience.
To mitigate the above problem stateless approach comes handy.
In this approach when a user logs in or done something, we are keeping track of the whole session in a separate database. (preferably NoSQL for Key-Value and simplicity and low latency). So every time request comes from a particular user, web server first checks the the DB for session details and responds accordingly.
Now after stateless implementation, UserA performs login in ServerA and when login succeeded it stores all the needed details to the database(like userId:{session_details}). Then due to high load, load balancer redirects UserA to ServerX. But this time ServerX goes first to DB and look through the session if it finds user logged in then it will redirects user to home/product page.
So in that way if we implement Vertical Scaling, each request will be independent of which machines it is was logged in or performed some actions as we keeping global track of the session via DB. So we can add as many machines we want to.
