is it possible, to host a minecraft server on a website? if so, then how?
You don't host anything on a "website", a "website" is an abstract created by the presence of inter-linked pages on a web server.
The server -- i.e. the underlying computer -- on which you host your website can, of course, be used to host a Minecraft server, but whether you have the appropriate access to it to enable it to do so is different and would depend on where you're getting web hosting from.
If u got SSH, FTP and more than 512 RAM than yes... Than no ;P
Though having server specs is a good indicator of whether you have a virtual server rather than simple website hosting space, a bigger concern is whether or not an admin can properly host if unable to differentiate between the two.
To make it simple, if you regard what you have purchased as a 'website'--it's probably just hosting space. This means you've paid or are paying maybe $5/mo rather than something like $25/mo, which would be closer to the expected cost of a server that dedicates resources to you, such as ram.
2. What kind of server is this? You need specifics!
3. Do you have SSH access?
4. Is it a cloud server or VPS?
If your webserver is a VPS then it very well might be possible, however you do need nearly root access. This means you would need access to a console, your java installation, and ALL folder access. Not just your apache folder. Cloud servers a bit different, you technically might be able to still do it considering some cloud servers are able to run applications on however, it will have very limited resources.
All in all, its best NOT to run a JVM (Java Virtual Machine) on the same server your running a webserver. As they may conflict in resources and also it destroys your bandwidth. Theres also the troubles with some plugins using webports for communications. Though these plugins typically are configurable.
Conclusion: If your able to, which in most cases your not. I would advise AGAINST it.
You can host a website on most minecraft servers, but not a minecraft server on most web hosting plans. You need SSH and FTP/SFTP/SCP access to the server to do it. You need either a dedicated server, or a VPS.
I'm 100% sure you can do it if you have FTP / SSH access to the server that runs your website.
Just because he can FTP to a server doesn't mean he can host a minecraft server. It depends if the server is has is under his control or not. If he owns it, he can put whatever he wants on it. If its just a webhosting server, then no he can't.