Intelligence measures a character’s analytical ability, their memory, and their ability to reason logically. A character with high Intelligence knows many facts and pieces of trivia, can estimate the value of items, can communicate nonverbally, and they are often good at puzzles, games of skill, researching, investigation, forgery, and investigation.
Intelligence is most important for Artificers, for Wizards, and for Fighters who select the Eldritch Knight subclass. For those characters, Intelligence will make their spellcasting more effective.
Arcana, History, Investigation, Nature, and Religion are all tied to Intelligence.
Arcana measures knowledge of magic and how it works, magical symbols and traditions, and other planes of existence and their inhabitants.
Arcana also allows characters to identify spells as they are being cast, which can be helpful for characters who can cast Counterspell, for responding to the effects of spells with ongoing effects like illusions, and for handling spells without obvious visual effects like curses. Identifying spells using Arcana is explained in detail in Xanathar’s Guide to Everything.
History measures your knowledge of the past: wars both recent and ancient, lost kingdoms, ancient lore, and all manner of events which took place in the past.
Investigation is used to search for clues, and to make deductions based on those clues. Investigation can be used to search documents for a piece of information, to determine where someone has been based on the state of their clothing, or to perform other acts of deductive reasoning like identifying some types of illusions.
Nature measures knowledge of the natural world; plants, animals, geography, terrain, weather, and natural cycles like tides and seasons.
Religion measures knowledge of deities, rites, prayers, religious orders and their organizations and activities, holy symbols, and other topics related to religion.