To conceive is to come up with an idea. If you conceive a plan for your little brother's birthday, you dream up the perfect party, complete with a magician, rented ponies, and a cake shaped like a rocket.
Latin roots for conceive (by way of French) point to "take into" either "the womb" or "the mind." An idea is sometimes called "a seed" or "the seed of an idea," and conceive means to produce something from inside the mind — or to become pregnant. Another expression is "pregnant with ideas" or "pregnant with possibilities," and someone who can "conceive of a thousand ways" to solve a problem or design something is full of new ideas.