Hashes provide constant time lookups by key as opposed to constant time lookups by index. Imagine if your dictionary were 0: Apple, 1: Ball, 2: Cat, 3: Dog. Find the word at index #2. That's done in constant time. Now find for me Cat. You have to either do a linear search, or a binary search to find it (linear time, or log2(n) time. You would never remember that 4200 is Quagmire, so you end up doing time-consuming searches a lot.
Now let's organize your dictionary like this: "Apple: A fruit. Ball: A toy. Cat: A skittish animal. Dog: A loyal animal. ..... Quagmire: A difficult situation". Quick, find if Quagmire is in the dictionary. Wow, we just did it in constant time (no searching), using a hash.
That turns out to be really, REALLY useful. We're not always just looking up words in dictionaries. We're referring to attributes in objects, we're manipulating sets, we're memoizing and caching, and we're even implementing variable systems (Perl's package globals reside in a glorified hash, internally).
In computer science one would look at hashes as yet another datastructure. And for many problems, selecting the right data structure is 9/10ths of the solution. As you get into programming, I recommend getting a good introductory book on data structures and algorithms. I wish I had a suggestion for you. Mastering Algorithms with Perl is probably a little advanced at this point, and it's getting a little old too. But start looking at, well, what is an array, and what are its characteristics? What is a linked list, and what are its characteristics? Binary Tree, Hash, and so on.
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