Katakana can be used for a lot of different purposes. Most commonly, it is used for loanwords and expressing non-Japanese names in a Japanese context, but it is also used for emphasis. Its use for emphasis relies on the characteristics of katakana: the sharp, defined look and its phonetic nature which makes it perfect for brand names.
Take this Suntory Malt Whisky Advertisement. The word かっこいい (meaning handsome, stylish, or cool), is in this case presented as カッコイイ. Notice the aesthetic of the ad as a whole. The image conveys a specific sharpness. The man's face is as well defined as the glass he's holding. And to match this image, katakana is used to make the word かっこいい look like it's definition. In the same way that typography is key to advertisements in English, choice of script is equally important to advertisements in Japanese. Katakana makes the ad's message more immediate and consistent, and consequently, very effective.
In addition to emphasizing Japanese words, katakana is very important for its use in brand names. This is an image of a record of music from the anime Samurai Champloo. Anime names are quite often written in katakana, to emphasize the sound of the name rather than its meaning, and to make it more readable (compared to kanji). Samurai Champloo is even stylized in romaji as well. Like the Suntory ad, the katakana has a sharper look than the equivalent さむらいちゃんぷるー. This emphasis makes katakana in brand names incredibly popular. Whereas hiragana words have no identity but a strong meaning, katakana have a strong identity but very little meaning. "Champloo" is an Okinawan word meaning "somegthing mixed" that is the name of a Okinawan stir-fry dish. While a few may know that and understand its relevance to the show, everyone can understand that Champloo distinguishes the name from other animes, which is why the katakana is such a good choice.
Our textbook readings describe katakana in different manners because while it is used for loanwords, emphasis, and onomatopoeia directly, its use in the categories serve a wider category of goals and bring with it a wider variety of meanings. All of them may explain the three cases in which katakana is used, but explaining why it is used is a more difficult task to do in such a short description, and is better grasped by looking at examples of katakana within Japanese culture.