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.

When a task or duty is so difficult to perform that doing so feels like a burden, it may be best described as onerous. Onerous comes from the Latin word for "burden," onus, which is used in English with the same meaning. A burden is something that is oppressively heavy, and indeed, when we use the word onerous, we evoke the idea of heaviness: an onerous undertaking is one so riddled or "heavy" with hardships it is difficult to bear. Onerous is also used to describe agreements, contracts, or guidelines that are so bogged down with legal obligations or restrictions, the intended benefits or advantages are outweighed.

There are many types of knowledge, and erudition is one of them. Erudition is a thorough, formal, and profound sort of knowledge obtained by extensive research. The term is often used to discuss knowledge in fields other than those of mathematics and the physical sciences—so you're more likely to encounter it in discussion of philosophy or literature than in discussion of biology. Erudition is not a high-frequency word in English, but when it is used, it's likely to be in a context of glowing appreciation, as something that inspires respect or awe.

To call something consequential is to say that it's significant or important, with special attention to the consequences, or effects and outcomes, it brings. The primary meaning of consequential is "following as an effect, result, or outcome." The term ultimately comes from the Latin verb sequī meaning "to follow," which is also the source of the word sequence. A consequential decision is one that will significantly shape what follows. An event that is politically consequential is one that might alter the course of politics in some significant way, and something that proves consequential is revealed over time to have been an important or determining factor in the course of events.

To ensure something is to guarantee or make certain that it will happen. For instance, someone heading to a job interview might leave their house an hour early to ensure that they arrive on time. The verb secure is used with a very similar meaning, but often implies bringing something about, or getting ahold of something. A critically acclaimed book might secure an author's reputation, or an impressive play in a championship game might secure a victory. Additionally, secure is often used to talk about safety, both as a verb and an adjective, e.g. "The townspeople used sandbags to secure the town during the flood; as a result they all felt more secure."