Evidence is broadly defined as any material observation used to support the truth or falsity of an hypothesis.
In law, evidence consists of assertions of fact or opinion provided to the court in support of, or in opposition to, the case of a party.
In science, evidence is more tightly defined to mean observations that are correctly documented and gathered systematically. "Anecdotal evidence," or observations that were gathered outside the scope of a formal study, does not count as scientific evidence, since the observations may be from an unreliable source, and also may have been interpreted incorrectly due to unseen factors. A simple example is that if it starts to rain while one is washing one's car, that is anecdotal evidence for the hypothesis that car washing brings rain.
Anecdotal evidence is distinct from scientific evidence as anecdotal evidence is not repeatable; for example, if a scientist observes some "freak occurrence," that does not count as scientific evidence unless the scientist can reproduce the occurrence within the bounds of a formal study, ensuring that the problems associated with anecdotal evidence (coincidence and unreliability) are not an issue.
Etymologically, the English word evidence ultimately derives from the Latin phrase ex videns, meaning from seeing. So evidence is any way in which we can see that something is so — however, the seeing is metaphorical, and includes ways of acquiring knowledge which do not involve sight at all.
Hebrews 11:1 (KJV) states "Now faith is the substance of things hoped for, the evidence of things not seen." Some interpret this passage as biblical endorsement for the idea that faith is evidence, that faith is a type of evidence. Others by contrast see faith and evidence as opposites, faith as being what you have when you don't have any evidence. The later view is that of those who reject faith, such as atheists; however, some fideists, such as those influenced by Søren Kierkegaard, would endorse the same dichotomy.
Evidence is distinct from proof. It is possible in both a court of law and scientific research that some evidence might appear to support one explanation and other evidence supports another explanation. Juries must weigh such conflicting evidence and decide which is more reliable and relevant. Scientists must also weigh such conflicting evidence, if not do more research to obtain more evidence. Often different opinions on which evidence carries more weight leads different scientists to different conclusions. Similarly, scientific opinions often change as more evidence comes to light.