Etymology is an area of linguistic science; it's the study of the origin of words and the ways in which their meanings and usages have changed over time. The etymology of a specific word traces the historical development of its meaning. Etymological study relies on attested forms -- that is, words as they were attested in writing throughout history. Because of this reliance on attested (written) forms, the study of English etymology helps explain why some words are written the way they are.
While many dictionaries include etymological information along with other aspects of a word, like pronunciation, definitions, and examples, not all do. Some dictionaries are exclusively etymological, including the Online Etymology Dictionary, an excellent resource for learning more about word origins. Compiled from a host of comprehensive etymological resources, the Online Etymology Dictionary is the only website of its kind. Not only can users search for English words, but also for historic roots (like the Old English word trēow), to see what modern words derive from that root.
Etymology is a major consideration in the word studies and spelling questions investigated on LEX: Linguist~Educator Exchange, a website dedicated to bringing language science to the language arts. Some pages on the website are tagged specifically as etymological and offer insights into the meaning, spelling, pronunciation, and usage of specific words or sets of words.
Etymological study can inspire more than just writing or usage. A few online resources also offer compelling visual representations of etymology. Real Spelling offers a gallery of short videos that explain orthographic etymology -- or how word histories and relationships between words explain their spellings. Illustrated Etymology offers a collection of visual explorations and celebrations of word histories as well.
What is the difference between "a hearty welcome" and "a cordial reception"? In a brief, action-packed history of the English language, Kate Gardoqui explains why these semantically equal phrases evoke such different images.
Gina Cooke wrote two other lessons for TED-Ed. Watch the one about why there is a b in doubt here, and the one about making sense of spelling here.