Minecraft server is a kind of server which allows online players to play online together.This type of server run on a minecraft server service which is virtual private server or is a kind of home machine.The server setting is bit different and you can check for the server set up here.
Setting up this type of minecraft server takes more time and do not try this if you do not more than basic computer skill.At first look for some online technical video or guide to set up the server. You can play and host in the same machine but you need to check whether your computer is very slow or not.If your computer is slow then it will create problem.
Many users using a same server in an wireless network is not recommended and it will create problem.If the number of players is more then you must need to use wired LAN.
To host this kind of minecraft server you need more memory in your computer.The size which is recommended is at least 4 GB.If you have more space then it is better for hosting.Still one question is not answered and that is actually how many servers you can support.To get this answer you can check here.
If you want to run it in a *NIX based server OS then you need the below configuration:
2.2Ghz Single-Core, 2GB RAM, A High-Speed internet connection (10MBp/s)
If you want to run it in a Windows based system then you need to have the below configuration 2.2Ghz Single-Core, 2GB RAM, A High-Speed internet connection (10MBp/s)
Renting Minecraft servers:
If your computer does not have enough configuration then you can also rent minecraft servers.Sometimes because of the internet connection people are not in a position to support that amount of players that they need.In that case they rent servers from hosting company.You should avoid that kind of sites that are not good.You can check those in Minecraft Server Forum.