Alphabets are just sets of symbols. Each symbol in our modern alphabet represents a sound. In all cases, these sounds are basic phonemes: simple sounds that can be combined to form words or varying complexity. The earliest alphabets were mainly just symbols for consonants, with no vowels included. Ths cn wrk fr wrtng, bt t mks t dffclt t rd. (This can work for writing, but it makes it difficult to read.) The introduction of letters to represent vowels made writing and reading more accurate. (It is actually worth pointing out that inventions such as spaces between words, punctuation and paragraphs are fairly modern inventions. Imagine trying to parse out the meaning of that vowel-less sentence without spaces!
Thscnwrkfrwrtngbttmkstsprdffclttrd is a nightmare compared to This can work for writing, but it makes it super difficult to read.)
So, the original alphabet(s) that ours is based on was fairly simple. Each letter represented a simple sound. The trick to understand is that the modern English alphabet (which is based on the Latin alphabet, which is based on the Greek alphabet, which is named for the first two letters, alpha and beta,) is one that grew. For the most part, English is a language that grew out of the fusion of Germanic and Latin and Greek, plus a few other tongues thrown in for variety. Why does this matter?
Well, languages grow and change over time. But the particulars of a language are usually limited by the original set of rules that the language grew from, and this can include sounds. There are places in the world where the antive languages can include sounds or tones that are not familiar to us as English speakers. Some asian languages are hugely tonal, where the meaning of a particular set of phonemes can be different based on HOW it is said. In some ways, speaking in those cases is more akin to singing. On the other hand, some of those languages lack certain sounds, such as Ell (L). There are plenty of sounds that we could use as phonemes, but we don't. Most human languages don't use clicking or popping or whistling noises...but there is no logical reason they couldn't. They just didn't grow and evovle to include certain sounds.
So, back to Latin, and their alphabet. Going waaaay far back, the Latins used an alphabet that only included 21 sounds. The classical Latin that the Romans spoke used 27 sounds. When the Romans spread out to conquer most of Europe and the Mediterranean, they spread their alphabet with them. As the Latin language began fragmenting into the various Romance (Roman) languages after the fall of the Roman Empire, the new European Romance languages of French, Italian, Spanish, etc. continued to use the old Latin alphabet. This was fine, because they naturally shared most of the sounds from the Latin language.
But then we get to England. England (and the Celtic tribes who lived there) had been conquered by the Romans in the time of Caesar, and so had inherited the Latin Alphabet. But England was invaded in waves by sea raiders from the north of Europe (Vikings!) as well as conquered by Normans in 1066 (French Vikings!) who imported French. So, England's language incorporated a lot from these other languages: Latin, Germanic, and French. For the most part, this was not a big deal. There was enough similarity in sounds among these languages that the Latin Alphabet could be used to represent them all in writing, especially by combining two letters (also known as a digraph.) This, by the way, is one of the reasons English is so weird. Why do we have different ways of writing the same sound? Why does threw sound just like through? Well, those words entered English from different sources, from different languages.
For the most part, less common sounds in English like "ch" and "gh" are still written as digraphs. But w is somewhat special. See, in Latin, there was no "w" sound. Instead, they used a "u" sound, spelled with a v. In German, there are LOTS of "w" sounds. So, when writers in German and English tried to write a symbol to indicate the "w" sound, they used a digraph. In this case, they used the same letter twice. The "u" was probably chosen because there is a similarity between the "u" sounds and the "w" sound. (In a sense, the w "wha" sound is a version of a u "you" sound where the lips are brought close to each other at the end. In any case, the "w" sound entered the written language as uu. Over time, it was used frequently enough in writing and (especially) printing that it deserved its own typeset die. This meant that printers went to the trouble of making a block with two u's on it when setting up something to print, instead of just using two blocks that each had the u letter on them. Over time, printers and scribes squished the two u's so close together that they formed a single unit, and a new letter was born. The fact that we use the name "Double-u" simply reflects how they originally wrote the sound out, with double-u's.
So, short answer? Historical accident. Ain't language neat?