Randomised
A randomised study is one in which participants are assigned to groups by chance rather than by choice.
Randomisation is what allows a difference between groups to be attributed to the treatment rather than to the kinds of people who chose it. Without it, the people who opted into something may differ systematically from those who did not.
It is the reason a randomised trial carries more weight than an observational study of the same size, and why 'people who took X did better' is a much weaker claim than it sounds.
What it is not
Randomised does not mean large, long, or well conducted. A small randomised trial can still be underpowered, brief, or measuring something other than the outcome you care about.