What is the difference between dynamic and static IP addresses ?
IP address is a 32-bit number that identifies each client or server on the Internet. This definition is based on the current version 4 of the Internet Protocol (IPv4). Each packet sent across the Internet includes the sender's and receiver's IP addresses in order to route the packets correctly. You can think of it as the Internet equivalent of a phone number where you can be reached. IPv4 addresses are divided into 4 parts, each ranging from 0 to 255, separated by dots, for example: 192.168.0.1
Dynamic IP addresses can change each time you connect to the Internet, while static IP addresses are reserved for you statically and don't change over time.
Residential Internet connections, whether broadband or dialup usually use dynamic IP addresses, while commercial leased lines and servers have static IPs, so they can always be reached at the same address.
The need for dynamic IP addresses arises from the limited number of IP addresses available in IPv4 (Internet Protocol version 4). Theoretically, there can be about four billion IPs in the Internet, however, the actual number is much lower for various reasons. Something had to be done to ensure supply of address space, at least until IPv6 is widely implemented on the Internet, allowing for 128bit IP addresses. The limited IP address space is one of the reasons for the wide use of NAT routers, as well as DHCP and leasing of dynamic IP addresses.
With dynamic IP addressing, there is a pool of IPs that your ISP can assign to users. When you connect to the Internet, your computer is leased one IP address from that pool for a number of hours. When you disconnect, or when the lease expires the IP address is freed and put back into the pool of available IPs. That way, ISPs can have more subscribers than number of IP addresses (as long as they don't all connect to the Internet at the same time) and ease IP maintenance.
Even with always-on broadband connections, it's easy to just lease IP addresses as needed. That's why the DHCP dynamic IP addressing is widely used today, especially for residential connections where users don't run servers. The downside is, your IP address, or "phone number" if you will, can change any time you get disconnected, there is a power outage, ISP maintenance, etc. The fact that you get disconnected does not necessarily mean the IP address is going to change, just as the fact that you get the same IP address does not mean it is assigned statically.