A Virtual Private Server (VPS) is an independent, virtual partition on a physical server. Think of a server with different "containers" within it. When you sign up for HostPapa VPS hosting, you get one of these containers to manage as you wish—install applications or scripts, and arrange your web files the way you want. It's private, secure, and flexible.
Migration or transfer services are often free or offered at a reasonable fee. These services help move your existing site to the new hosting provider. They can save a huge amount of hassle. Just remember that the migration process is often automated, and may fit in with the host's processes and needs rather than yours. Not everything may migrate, and you may find the organization of the newly migrated site makes for harder maintenance in the long run.
A Content Distribution Network (CDN) is a network of servers distributed geographically. The purpose of a CDN is to deliver content on the internet much faster. If a user in Toronto is trying to access your website, the closest server to them will take care of this. But someone coming to your website from Sydney, Australia, will be catered to by a server closest to them. The main host server holds your website content, and all the other servers have a cached version each.