Explanandum is a Latin term used in logic and philosophy of science; it is actually one half of a pair: explanandum and explanans.
The explanandum is the object or event that need to be explained; the explanans is the explanation.
Explanandum: Spider-Man can climb buildings using webs he shoots from his hands...
Explanans: Because he was bitten by a radioactive spider.
This is actually a rather poor example of explanans, as these terms are used specifically to describe the proper parts of a scientific explanation. While there have been a number of papers written on what makes a proper explanans, we could do worse than to use Karl Popper's summary of the conditions for a proper scientific explanation:
(a) the explanans must be true or at least taken for granted as true;
(b) the explanandum is a logical consequence of the explanans;
(c) the explanans is tested independently of the explanandum.
In this case, it appears that the Spider-man example fails criteria (a) -- Spider-man doesn't actually exist. It also fails criteria (b) -- it does not follow that being bitten by a radioactive spider would turn you into Spider-Man. And finally, to the best of my knowledge, no one has run tests on Spider-Man creation, causing our claim to fail on criteria (c) as well.
Carl Hempel and Paul Oppenheim added another criteria; that a good explanans should also contain general laws -- for example, our Spider-Man example should include not only "because he was bitten by a radioactive spider", but also "radioactive creatures always pass plot-relevant mutations onto their prey". However it is arguable that this is a reasonable interpretation of criteria (b), as in scientific arguments building logical consequences does require references to general laws.
This is probably not a new idea for most of us, simple a different way of expressing a familiar idea: if you see an event and then look for an explanation, you might speak of the explanandum and explanans; if you have an explanation and look for the event, you would speak of a prediction and an experiment. In both cases, the actual event and the explanation for the event is the same -- or in other words, a well-constructed explanans should be sufficient to predict real-world outcomes.
In our everyday lives we simplify things greatly; an explanation like "I'm sick / because you sneezed on me" does not meet the strict criteria of a full explanandum. We simply assume that the listener understands the unspoken "and my sickness is caused by the flu virus, and you are carrying the flu virus, and the virus can be transmitted by sneezing, etc." This does not make the shortened version a bad explanans, as long as the simplification is understood by both the listener and the speaker.
The plural of explanandum is explananda; the plural of explanans is explanantia.
Confusingly, there is another closely related set of terms, also descended from the Latin explanare: the explicandum and the explicans are used in the analysis of meaning, while explanandum and explanans are used specifically in the philosophy of science.
You may also be interested in the closely related terms definiendum and definiens, a pair that does for 'define' what explanandum and explanans do for 'explain'.