Normally when you log into your ISP either by dial-up or with an ADSL or Cable router, the ISP will allocate a random IP address out of a pool of addresses via its DHCP (Dynamic Host Configuration Protocol) server. When the connection is dropped (as in dial-up) the same IP address that was held by you goes back into the pool and can be allocated to someone else. In the case of a router, it will hold the address until it is reset.
A static IP address is one that your ISP will allocate to you and this address will not change. The address will remain exclusively yours for the length of the contract. Static IP addresses tend to be expensive and are usually only used for commercial purposes. For normal day-to-day use, dynamic IP addressing is the norm rather than the exception.