A dedicated IP address is unique to your domain and web space - you do not share it with any other web user or domain.
If someone types in the numeric form of your IP address, your domain will always appear in their browser. Exclusive IP addresses are expensive and normally only seen on large ecommerce sites like amazon.com.
Many search engines such as Google rank websites with their own dedicated IP address higher than websites that share an IP address. They also offer practical advantages including the ability to host your own SSL certificate and host anonymous FTP.