Hiragana and katakana are both phonetic (sound-based) writing systems. Furigana is used to show the phonetic reading of a kanji (or sometimes even Latin lettering).
It is not used with katakana because katakana is already phonetic, so its pronunciation is unambiguous. For example, my name (Eric), in katakana, would be エリック. You could express this phonetically equivalently in hiragana as えりっく. The katakana in your example would be phonetically equivalent to しゅがあ. I would recommend reading about the Japanese writing system to learn about katakana and hiragana.
On the other hand, kanji are very difficult by comparison. Students learn around 2,000 kanji over the course of many, many years, while hiragana and katakana take essentially no longer than first year. So, if the kanji is a very high grade level, the person may not know it at all, but may know the word that it represents if they know the sound of it.
Kanji also often have different readings. Notably, they usually have a Chinese reading and a Japanese reading, but they can have multiple of these as well. Take 食 for example. た and しょく are among its many readings.
In fact, the Wikipedia article you already linked states this nice and concisely:
In modern Japanese, it is mostly used to gloss rare kanji, to clarify rare, nonstandard or ambiguous kanji readings, or in children's or learners' materials.
You will notice that manga published in shounen magazines will (almost?) always have furigana, while it's far less common in seinen magazine manga, simply because by the upper end of the seinen age range, people know enough kanji to read it all. (I have noticed a few in seinen books, but as far as I know they're less common, such as the kanji for もらう.)