In short
A randomized controlled trial (RCT) is a study design in which participants are randomly assigned to receive either the intervention being tested or a comparison (control) condition, allowing researchers to isolate the treatment's effect from other influences.
Random assignment is the key design feature: because each participant has an equal, chance-determined probability of ending up in either group, known and unknown factors that could otherwise influence the outcome (age, baseline health, lifestyle, genetics) are, on average, distributed evenly between groups when the sample is large enough. This is what allows researchers to attribute a difference in outcomes between groups specifically to the intervention, rather than to some other pre-existing difference between the people who happened to receive it.
Well-designed RCTs typically add further controls to strengthen this isolation: blinding (participants, and ideally researchers assessing outcomes, don't know who received the active treatment) reduces the influence of expectation effects (including the placebo effect) on both participant-reported and researcher-assessed outcomes, and a control group receiving a placebo or the current standard treatment provides the comparison baseline needed to judge whether the intervention outperforms doing nothing or doing what's already standard.
RCTs are considered the strongest form of evidence for establishing that a specific intervention causes a specific outcome, which is why this site's evidence-grading framework requires repeated positive human RCT results — not observational data, and not animal or cell-culture data — for its highest grade. RCTs do have real limits: they are expensive and time-consuming, which is part of why very long-duration outcomes like human lifespan extension are extremely difficult to test this way, and a trial's results apply most directly to a population similar to the one actually studied, which is why the specific population, dose, and duration of a trial always matter when interpreting what it does and doesn't show.