An 'A' Record is similar to a CNAME Record, in that it helps the DNS point what you type into your web browser, to the website you want to view. Whereas a CNAME record points the www part of the web address, an 'A' Record can point the domain name directly at the server.
For example, if I want our web address to be illuminateict.org.uk (without the www at the start), then I'd need to use an 'A' record.
At the moment, we find it slightly easier to point www addresses using CNAME records, but we're looking at ways we can improve things in the future so that even if you omit the www from the address, you'll still arrive at the right site.