What is dedicated hosting?
A dedicated server is owned by the hosting company but rented out to you for a monthly fee along with an allotment of bandwidth which you can use with it. This means that you get a whole server to yourself to use for what you desire, this is needed for scripts which use a lot of server resources (for example large message boards, for one of which I pay for a dedicated server).
As a customer, you would have full control over the server and could change the configuration as required, a facility not available when you have to share a server with others. With a dedicated server, the web hosting company is responsible for the hardware as they own it, not the customer.
What are the advantages of it?
You can do anything you like on it that you like.
This means that you can login to the server, set up programs as you desire, then run them without having to worry about the effects on server resources for other people. You can run games servers (for games such as Half-Life, etc), IRC servers or bots, or just run a web server which uses a lot of resources (and with a special setup which isn’t found in shared hosting).
Do note that most hosts have acceptable use policies (AUPs) which state that illegal content is not allowed, and in some cases they prohibit connecting to Internet Relay Chat (IRC).
What are the disadvantages?
The main disadvantage is the cost, which will put many people off getting one. The cheapest seem to come at about $50/month, and the most expensive cost thousands of dollars each month. The price can be reflective of the quality (such as the cost of running - or your host renting a space in - the datacentre, the hardware in the server, the technical support provided by your host and so on), alternatively it can just be an over inflated price for what is a poor quality product. It’s important to compare the prices and packages offered from several companies before coming to a decision, also you should ask your friends if they have any opinions on the matter, and research information about the hosting companies and datacentres - are the constantly offline due to DDOS attacks? do they have a poor record of customer service?
Another disadvantage is the added responsibility involved in keeping the software on your server secure, for example you may have to update builds of apache, control panel software, etc as security holes are found.
Is it for me?
That depends, if you want to a game server then you’ll need one - but it may be easier for you to buy one from a dedicated games server comapny, they know their stuff and would probably be able to install and configure the servers for you. However they would place restrictions on what you could do with the server and maybe the setup.
If you want to run a small IRC server, bot or bouncer then you would probably be easiest paying a smaller fee to hire one of those from an IRC or shell provider company, also you don’t have to worry about restrictive datacentre acceptable use policies which prohibit IRC use.
If you are starting a small web forum or site then you probably won’t need one initially, wait until it grows and you can determine if you need the server to ensure further growth is ok.
Otherwise you could possibly look into getting one, you could even email hosting providers asking what package they think your site would require (although take their replies with a pinch of salt, they could try to sell you stuff you don’t actually need).