Proof of fact(s) presented at a trial.
Neatly divided into the most prevalent, direct evidence, and the slightly more difficult, circumstantial evidence.
A judge, at the commencement of a trial, is like an empty scale - the scales of justice!
She knows nothing at that point so the scale is perfectly balanced.
It is up to the two opposing sides to teeter the scale one way or another with evidence so that at the end of the hearing, she can determine what the truth likely is and can render judgment on a preponderance of what she's heard or seen: the evidence.
The best and most common method is by oral testimony; where you have an eye-witness swear to tell the truth and to then relate to the court (or jury) their experience.
Evidence is essential in convincing the judge or jury of your facts as the judge (or jury) is expected to start off with a blank slate; no preconceived idea or knowledge of the facts.
So it is up to the opposing parties to prove (by providing evidence), to the satisfaction of the court (or jury), the facts needed to support their respective cases.
In a civil suit, the plaintiff has the burden of proof so in the event of a tie in the evidence, the plaintiff loses.
In a criminal trial, the burden (a different burden: beyond a reasonable doubt), is on the prosecutor.
Besides oral testimony, an object can be deposited with the court (eg. a signed contract). This is an example of direct evidence, sometimes called "real evidence."
In other rarer cases, evidence can be circumstantial.