Put simply, self-hosting just means that you are "hosting" a website yourself on a server that you control.
The opposite of self-hosting is "managed" hosting, like Wordpress.com or Ghost(Pro). These services let you create sites through their service and they handle everything for you.
Ghost is open-source software that can be downloaded for free. You are then allowed to install it anywhere you like, on any server; this is self-hosting!
The main benefit of self-hosting is the much lower cost than using a managed host. Costs are lower because you are only paying for the server and not any of the ongoing maintenance or updates that managed hosts offer.
If you self-host, you own and are responsible for the server, plus you'll need to do the initial installation and any future code updates.
Gloat is a pay-as-you-go developer service, offering personal Ghost installations and updates.
Get a self-hosted site up and running for a simple one-off fee ($59), and pay just $5/month for hosting on your own server. If you want to update Ghost in the future, just buy an update ($19), or sign up to a Gloat maintenance package for ongoing support.
1) Managed hosting
The most popular Ghost host is The Ghost Foundation's own Ghost(Pro). This is "managed" hosting, and offers server maintenance, frequent Ghost updates and some ongoing security measures. Pricing ranges from $36/month to $249/month.
Gloat now offers managed hosting for $149/year. More details at gloathosting.com.
There are also other managed Ghost hosts like Midnight, which has pricing starting at $15/month.
2) Do everything yourself
You could of course download Ghost for free and set up your own server. This would cost you absolutely nothing apart from a monthly hosting fee, which can be as low as a few dollars. However, you need to be comfortable logging into servers, installing software and configuring Ghost.
3) Use Gloat for simple setups paired with cheaper hosting
Gloat aims to sit in between a (more expensive) managed host and a (difficult to set up) self-hosted site. It provides you the opportunity of accessing cheap hosting without having to be a developer.