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!

To improve something is to make it better or bring it into a more desirable condition. Ameliorate shares this broad sense, but this formal verb is typically used to discuss circumstances that are more dire than what you might find with improve. For instance, you may hear of improving a workflow, or improving sound quality, but it is less likely that you'll hear ameliorate used in everyday contexts such as these. More commonly, you'll find ameliorate in discussion of oppressive, unjust, or difficult conditions, such as those brought by social or economic inequality or environmental degradation.