Dynamic IP Address:
The Dynamic IP is the one which changes when you restart your modem / router.
By default, all DSL connections are provided Dynamic IP.

Static IP Address:
The Static IP is the one which does not change when you restart your modem / router.
To get a Static IP, you have to contact your ISP and request them to provide you a Static IP.
Most ISPs charge a monthly fee for Static IP in addition to Internet Connection charges.
A Static IP is needed when

The IP Addresses referred above are Public IP Addresses which are controlled by ISPs.
To find the difference between Private and Public IP Address: What is the difference between Private and Public IP Address

To find your Public IP Address: How to find out your Public IP Address