According to the AWS documentation "any data stored in the RAM of the host computer or the instance store volumes of the host computer is gone." Does this mean that the web application I installed on my EC2 instance will be deleted if I stop running my instance?
An Amazon EC2 instance is just like a normal computer. If you turn it off, anything in RAM is lost. Also, if you reboot either computer, the contents of RAM is lost (well, more like 'forgotten', but effectively the same).
Just like your home computer, if you reboot or stop/start an EC2 instance, it boots up again. Whatever software you have installed on the computer is still there. However, applications you were running will only start if you have configured a startup script to run the app again.
Typically, when software such as a web server is installed on a computer, it is configured to automatically start again when the computer is turned on/rebooted in future.
Elastic Block Store (EBS) disk volumes act just like a disk in a normal computer. If an EC2 instance is stopped and later started again, the contents of the disk is still there, unchanged.
Bottom line: It's just like a home computer. Don't panic.