"man uname" will explain the output in more detail, but uname -a gives you the name of your machine, the kernel version, the processor architecture and so on.
For the distribution, watch the messages at boot-up. Also it may be on screen if you use the graphical log-in. Failing that have a look in /etc. I run slackware and there's a file there called /etc/slackware-version, other distributions probably do something similar.