It will come to the time that you won't be able to run any command that is required creating tmp file when you have no space on your EC2 instance. Once it happens, you can't even start/restart web server or mysql.
Run following 2 commands to check your disk status:
$ df -h
$ df -i
df -i . checks your inodes. what are inodes?
You might have disk space, but you can't do anything if no more inodes space.
To solve this problem:
1. increase your Volumn by modify your EC2 Block Volumn size.
2. delete some file on existing sever to free up some space for you to run EC2 (resizing file system)
after that you have done above, check with
$ df -i
$ df -h
to make sure you are all good.