Evidence is the concrete facts used to support a claim. Ideally, evidence is something everyone agrees on, or something that anyone could, with sufficient training and equipment, verify for themselves.
Evidence comes in many types, which I discuss in detail here.
At its most basic, evidence is something that can be perceived with the senses. A great deal of scientific evidence is observable phenomena, like the change in color when two chemicals are mixed in an experiment, or the light emitted by a distant star, or the structure of bones in a fossil. In some cases, though, what you’re observing is very removed from the claim. For example, if I say “Einstein said that space is curved” as a fact to support my claim, the observable fact is the written record of what Einstein said, not a physical phenomenon that relates directly to my claim.
There is no clear-cut line between a claim and a “fact.” Things that are facts in one context might be claims in another. For example, “the earth orbits the sun” was once a claim (i.e. an unproven or controversial assertion), but now nearly everyone accepts it as a fact.