To explain is to make clear something that is not known or understood. A parent might explain to a disbelieving child why they cannot have ice cream for dinner (no nutritional value!). To expound is to give a methodical, detailed, scholarly explanation of something. It is a more elaborate action, with a slightly performative or presentational sense. A professor might expound theories, doctrines, or philosophies with lengthy verbosity. Legal experts might expound a law, and religious scholars might expound Scripture. But we also find it used humorously on occasion, in a slightly teasing or self-deprecating manner. While the use of expound with a preposition, as in expound on or expound upon, has some critics, pairings such as these have become increasingly common and are sure to be understood just fine.
To hope for something is to desire it with only some expectation that it will happen. It conveys a feeling of longing or wishfulness. The verb aspire nudges desire toward action, implying an eagerness and drive to make it so. The work that goes into making an aspiration real may even leave you breathless. After all, aspire comes from the Latin verb aspīrāre "to breathe upon" or "to pant after." Consider the lofty aspirations of the dog who pants after the squirrel; much like Fido, when we aspire to something, we are working to attain it.
Something that is fun provides enjoyment or amusement. Something that is convivial is friendly and agreeable, or festive. Convivial is a warm and social term; it's most often used to talk about gatherings of people who are in high spirits and enjoying one another's company, often sharing in a meal or refreshments. Its gregarious nature makes sense given its origin: convivial comes from the Latin noun convīvium meaning "feast," which derives from the verb convīvere "to live together, to dine together." When describing a person, convivial means "merry company, jovial." Convivial is good company any time of year, but given its appetite for feasting and gathering, it's no wonder we hear convivial a little more around the holidays!