A dynamic IP is one that changes every time you connect to the network and a static IP is one that remains the same no matter how many times you connect and disconnect from the network. Whether you have a static or dynamic IP address is up to the administrator of the said network.
A dynamic IP changes every time you connect to the network; this is a method of freeing up IP addresses when the number of clients that connect the network is greater than what it can usually handle. This can be seen in wireless access points where there could be a great number of users but not at the same time. The control and distribution of dynamic addresses is often handled by a DHCP (Dynamic Host Configuration Protocol) server which keeps track of which addresses are free and which ones are being used. Even though a DHCP server is meant for sending out dynamic IP addresses, it can also be used to assign static ones.
A static IP address can be acquired via DHCP when the administrator knows the MAC address of your network card is and assign a specific IP address to that. After that, you would get that specific IP address every time you connect and it is reserved for you only and nobody can use it. Another method of setting a static IP is to manually set it on your network card. You just have to be careful not to assign the same IP address to two or more computers or assign an IP address that is included in the DHCP pool.
There is also an advantage when having a static IP address when connected to the Internet. When running your own server, a static IP address would mean that you only need to have the DNS point to your IP address and you are done. With dynamic IP addresses, you would need to utilize a dynamic DNS service that you can update with your new IP address every time you connect.
Although having a static IP address has some advantages of its own, it is not necessary for the usual everyday use at home or in the office. Having a dynamic IP address in these cases is not a cause for concern and should just be left as it is. But for those who do need to have a static IP address, you might try asking your ISP if they can provide you with one for a fee