Okay first thing I will point out is that it appears as though they are using the term "domain cluster" to denote their cluster of DNS servers and are basically saying that you don't need to set it up with anyone else as you can set it up with them.
What is DNS?
DNS stands for Domain Name System and is used to resolve domain names into the IP addresses for the servers that are hosting them. A common analogy is telephone numbers and the phone book. You live in a town with millions of people in it and each person has a telephone number (ip address), now obviously you can't memorise all the phone numbers, but what you do have is a phone book (dns) with everyones names and their corresponding phone numbers, so when you want to call someone and you don't know the number you look up their name and their phone number is right there.
Now in the most basic sense DNS is very similar. Servers on the internet are connected to with their IP addresses (such as 22.214.171.124), but expecting someone to remember the IP address of the sites they want to connect to is asking too much so this is where DNS comes in. A company registers their domain and configures their DNS records, which are basically a list of the web addresses they have available to connect to, and the corresponding IP addresses for the servers hosting each of those web addresses. When you type a domain name into your browser (such as www.google.com) your browser connects to a DNS server and asks it what the IP address is for www.google.com, putting aside DNS forwarding and root zone servers the DNS server through back end processes gets the IP address for www.google.com.au and returns it to your browser so the connection can be made.
Can You Host a Website Without DNS?
Yes you can, if you don't want people to easily connect to the website or you want them to have to type in an IP address every time they want to connect to it and don't want to run any other websites on the same server but as you can see this is not practical. In order to convert a domain name (www.google.com) into an IP address (126.96.36.199) you have to have a DNS server hosting the records for the google.com domain listing all the relevant records and corresponding IP addresses as required.
So Back to the "Domain Cluster"
While by and large hosting providers tend to keep to the well established terms such as calling a DNS hosting service a DNS hosting service some like to come up with strange new terms in order to make their services sound special and unique (marketing?). What it sounds like your web host is saying is that you don't have to set up a separate DNS hosting service somewhere else, that they support it. By referring to it as a cluster it sounds like they have multiple DNS servers set up to mirror records and provide a fault tolerant DNS system (a good thing) but basically what they are offering is DNS hosting on what they consider to be a better service that competing services.