Some 5e class descriptions have a little bit about the nature of magic as well and provide some narrative material to work with.
In the worlds of D&D, words and music are not just vibrations of air, but vocalizations with power all their own. The bard is a master of song, speech, and the magic they contain. Bards say that the multiverse was spoken into existence, that the words of the gods gave it shape, and that echoes of these primordial Words of Creation still resound throughout the cosmos. The music of bards is an attempt to snatch and harness those echoes, subtly woven into their spells and powers.
You have learned to untangle and reshape the fabric of reality in harmony with your wishes and music.
Divine magic, as the name suggests, is the power of the gods, flowing from them into the world. Clerics are conduits for that power, manifesting it as miraculous effects. The gods don't grant this power to everyone who seeks it, but only to those chosen to fulfill a high calling. Harnessing divine magic doesn't rely on study or training. A cleric might learn formulaic prayers and ancient rites, but the ability to cast cleric spells relies on devotion and an intuitive sense of a deity's wishes.
A s a conduit for divine power, you can cast cleric spells.
Druids revere nature above all, gaining their spells and other magical powers either from the force of nature itself or from a nature deity.
Drawing on the divine essence of nature itself, you can cast spells to shape that essence to your will.
Different paladins focus on various aspects of the cause of righteousness, but all are bound by the oaths that grant them power to do their sacred work. Although many paladins are devoted to gods of good, a paladin's power comes as much from a commitment to justice itself as it does from a god.
By 2nd level, you have learned to draw on divine magic through meditation and prayer to cast spells as a cleric does.
Thanks to their familiarity with the wilds, rangers acquire the ability to cast spells that harness nature's power, much as a druid does.
By the time you reach 2nd level, you have learned to use the magical essence of nature to cast spells, much as a druid does.
Magic is a part of every sorcerer, suffusing body, mind, and spirit with a latent power that waits to be tapped. Some sorcerers wield magic that springs from an ancient bloodline infused with the magic of dragons. Others carry a raw, uncontrolled magic within them, a chaotic storm that manifests in unexpected ways.
The appearance of sorcerous powers is wildly unpredictable. Some draconic bloodlines produce exactly one sorcerer in every generation, but in other lines of descent every individual is a sorcerer. Most of the time, the talents of sorcery appear as apparent flukes. Some sorcerers can't name the origin of their power, while others trace it to strange events in their own lives. The touch of a demon, the blessing of a dryad at a baby's birth, or a taste of the water from a mysterious spring might spark the gift of sorcery. So too might the gift of a deity of magic, exposure to the elemental forces of the Inner Planes or the maddening chaos of Limbo, or a glimpse into the inner workings of reality.
Sorcerers have no use for the spellbooks and ancient tomes of magic lore that wizards rely on, nor do they rely on a patron to grant their spells as warlocks do. By learning to harness and channel their own inborn magic, they can discover new and staggering ways to unleash that power.
An event in your past, or in the life of a parent or ancestor, left an indelible mark on you, infusing you with arcane magic. This font of magic, whatever its origin, fuels your spells.
A warlock is defined by a pact with an otherworldly being. Sometimes the relationship between warlock and patron is like that of a cleric and a deity, though the beings that serve as patrons for warlocks are not gods. A warlock might lead a cult dedicated to a demon prince, an archdevil, or an utterly alien entity-beings not typically served by clerics. More often, though, the arrangement is similar to that between a master and an apprentice. The warlock learns and grows in power, at the cost of occasional services performed on the patron's behalf.
The magic bestowed on a warlock ranges from minor but lasting alterations to the warlock's being (such as the ability to see in darkness or to read any language) to access to powerful spells.
Your arcane research and the magic bestowed on you by your patron have given you facility with spells.
I n your study of occult lore, you have unearthed eldritch invocations, fragments of forbidden knowledge that imbue you with an abiding magical ability.
Though the casting of a typical spell requires merely the utterance of a few strange words, fleeting gestures, and sometimes a pinch or clump of exotic materials, these surface components barely hint at the expertise attained after years of apprenticeship and countless hours of study.
The spells that you add to your spellbook as you gain levels reflect the arcane research you conduct on your own, as well as intellectual breakthroughs you have had about the nature of the multiverse.