IP Address
From HostPedia
All computers across the internet are assigned with a unique identifier called an "IP address". They are used like phone numbers in a phone book so other computers will be able to find them. An IP address could look like this: 65.425.422.31.
Any network device including routers, computers, infrastructure servers, printers, Internet fax machines, and even some telephone devices can have its own address that is unique within the scope of the specific network. Some IP addresses are intended to be unique within the scope of the global Internet, while others need to be unique only within the scope of an enterprise.
Static IP Address
A Static IP address is allocated to a specific device (computer, server,...) and does not change each time you access the Internet. A Static IP address can be used to run a web host for web sites or an email server.
Dynamic IP Address
A Dynamic IP address is an "IP address" that is temporarily assigned to a user or a device by their internet service provider each time they connect to the internet. The reason ISPs use this technic is simply beacuse it cuts down on the number of IP addresses these companies needs to pay for - since these companies knows the maximum number of concorent connection on a given day, it is usually works fine. It also cuts down on bandwidth usage by preventing consumers from hosting servers. Note: There are companies who offer services which allows users to update their DNS records dynamically and bypass this obsticle, see: Dynamic DNS Services.
Dedicated IP
A Dedicated IP address is an IP address that is assigned only to one web site, even if it is hosted on a shared server. A dedicated ip address is required for SSL certificated and it differs a web site from other websites which are hosted on the same server (some of these sites could belong to Bad Neighborhoods, a situation that cause email servers and web spiders to consider you legitimate web site as a spam site - and as a result to block email originated from you domain as well as damaging your SEO score). Most web hosting companies offer to their clients a shared ip address to cut down expenses, and a Dedicated IP comes only with additional payment. Even though it costs money, buying a dedicated ip address is highly recomended, prices are usually low. for example: HostGator.com charges only $2 a month for this service, ixWebHosting.com offers 8 Dedicated IP addresses for free with every shared hosting package.