Broken plurals (جمع التكسير) are one of the most distinctive features of Arabic morphology. Unlike sound plurals, which simply add a suffix to the singular form, broken plurals change the internal vowel pattern of the word. The singular form is essentially "broken" and rearranged into a new pattern.
For example, the singular كتاب (kitaab, book) becomes كُتُب (kutub, books), and رجل (rajul, man) becomes رجال (rijaal, men). Notice how the consonant root letters are preserved (ك-ت-ب and ر-ج-ل), but the vowels between them change. This internal modification is characteristic of Semitic languages and is a core topic in Sarf (morphology).
There are approximately 30 common broken plural patterns, though most everyday vocabulary uses about 10-12 of the most frequent ones. Some common patterns include: أفعال (af'aal) as in أقلام (pens), فُعُل (fu'ul) as in كُتُب (books), فِعال (fi'aal) as in جبال (mountains), and أفعِلة (af'ila) as in أسئلة (questions).
An important grammatical rule about broken plurals: when they refer to non-human entities, they are treated as feminine singular for purposes of agreement. So you say الكتب الجديدة (the new books), using the feminine singular adjective جديدة, not the plural جدد. This rule applies consistently across Arabic and is one of the first agreement rules you'll learn in Nahw.
While broken plurals require significant memorization, learning the common patterns helps enormously. Ilm Al Lughah's Sarf courses systematically teach these patterns, and the flashcard system reinforces them through spaced repetition. Over time, you'll develop an intuition for which pattern a given singular noun is likely to follow.