The thing that most people do not get at the beginning is that Matomo is a server software, so it means that you need to have it installed on a server in order to run it. This is what we call on-premise, it means installed on your own server.
Matomo is using mature technologies, so you can run it on the most simple servers. I have even one client some years ago who told me that it was running fine on Raspberry Pis.
In order to run Matomo 3.0, what you need at minimum is a webserver (Apache, Nginx…), PHP version 5.5.9 minimum and MySQL 5.5 or MariaDB with PHP extension pdo and pdo_mysql, or the mysqli extension.
Now, what you need to know is that those requirements will depend of the traffic you have, the more you have, then the highest the requirements are going to be. You will find on this page the defined requirement according to your traffic.