An IP address is a number that identifies each client or server on the internet; the internet equivalent of a telephone number. 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 fixed and don't change over time.
Residential internet connections usually use dynamic IP addresses, while commercial leased lines and servers (commonly belonging to medium/large companies) have static IPs, so they can always be reached at the same address.
With dynamic IP addressing, there is a pool of IPs that your ISP (Internet Service Provider) can assign to users. When you connect to the Internet, you computer is leased one IP address from that pool for a period of time. When you disconnect, or when the lease expires, the IP address is freed and put back into the pool of available IPs.
This means that your IP address can change any time you disconnect, or 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.