Can someone define the meaning of Dedicated Server, What is it really a server thats is just for you?

It is when you have one machine (server) for your web applications only (no other people's website or anything else there). It is dedicated to you only and you have admin access (Root and etc.) to server.

When you get dedicated server you have to be ready to manage it on your own.

There are also "Managed dedicated servers". That means that the server provider does server maintenances for you.

... you can also see Wikipedia (http://en.wikipedia.org/wiki/Dedicated_hosting_service)

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Do you want to buy it from the company?

You've already been given the answer in the posts above, use actually that's the case when you can use all the server's resources, but also the server administration becomes your responsibility or you can pay your host for server management.

VPS is a virtual dedicated server, that's the option cheaper than dedicated but giving you almost the same resources as dedicated server.

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Definitions of dedicated server on the Web:

* A server which is used solely for use by one organisation. The server is leased and stored in the data center of the host company.
http://www.webmotion.co.uk/resources/d.php

* For those customers that want the advantages of colocation without the hassles of purchasing their own server. See colocation.
http://www.cheapest-website-hosting.com/glossary-1-to-G.shtml

* A server that provides services for only one account or domain name.
http://www.verio.com/support/files/glossary.cfm

* The hosting company provides you with an entire hosting setup including your own server hardware that only you can use. This means a much faster loading time for your site because the entire computer is "dedicated" to running the server software. ...
http://www.theregister.co.uk/offers/hosting/glossary.html

* An advanced form of web hosting where the customer generally has complete control over the server. Dedicated Servers are typically housed in data centers. ...
http://www.ipowerweb.com/hostingdictionary/

* A computer—usually quite powerful—that is used solely as a network server. Compare nondedicated server.
http://www.microsoft.com/technet/prodtechnol/Visio/visio2002/plan/glossary.mspx

* means the computer server equipment provided by Delphi Creative for the sole use of a single customer;
http://www.delphicreative.co.uk/terms/delphi_hosting_terms.html

* a dedicated server is a server owned by 5points for your exclusive use.
datacenter.5points.net/datacenter/support/glossary/

* In the Web hosting business, a dedicated server refers to the rental and exclusive use of a computer that includes a Web server, related software, and connection to the Internet, housed in the Web hosting company's premises. ...
http://www.netunlimited.com/glossary.html

* A node on which applications are limited to maintaining network resources; no user applications are available.
http://www.connectworld.net/cgi-bin/iec/02GLSD.html

* A computer on a network that is assigned to function only as a resource server and cannot be used as a client.
https://www.watchguard.com/training/d.asp

* Similar to co-location, except that you lease or rent hardware from a Web host. The main advantage over co-location is easier upgrade and usually better support. ...
http://www.toplevelhosts.com/hostingterms.html

* A dedicated server is purchased by a company when they want more control of their server. What happens is they purchase or rent the hardware from the hosting company who then normally support and manage it.
http://www.theanswers.co.uk/glossary.html

* A dedicated server is a computer that only runs one type of server software, and is usually constructed according to the user's specifications. Dedicated servers are typically used for websites that have high traffic, and need many resources and much processing power.
guidex.biz/web_hosting/glossary.html