If you see yellowish skies on a humid, spring evening in Kansas, it is entirely conceivable that a tornado is in the making. That is to say, it's imaginable or even possible, so make sure you take every conceivable precaution.
If you conceive of something, you imagine or think of it. So, it makes sense that the adjective conceivable describes things that can be imagined or thought of. People often use the word conceivable in extreme contexts. If you look everywhere for your homework but still can't find it, you might declare, "I searched in every conceivable location! My homework must have disappeared." In response, your teacher might remark that disappearing homework is inconceivable, or "impossible to imagine."
