Well firstly, we need to understand that are basically 2 ways your Internet Service Provider (ISP) allocates IP addresses. For most home users, ISPs such as TSTT, provide an automatic allocation so everytime you connect to the internet via your dial up account or your DSL account, the ISP gives you a random IP from the list of IPs that they leased (rented). This type of IP address is referred to as a Dynamic IP address - key word here is "dynamic" which can be interpreted as "always changing" or random.
ISPs such as TSTT offer Static IP addresses to business DSL and this allows you to have a specific IP address that does not change which is highly useful if you would like to run a service such as a mail server. Also, these IP addresses are generally not tagged as SPAM related IP addresses. Talk to your ISP to find out more about static IP addresses.