When I took the JLPT N1 in Tokyo, I went into my assigned classroom at a small college campus near Shibuya station. I sat down at my desk and looked up towards the front of the classroom. For a few seconds I was so confused, as something like this was written on the board:

けいたいでんわのでんげんをきってください

That sentence (“Please switch off your mobile phones.”) is written entirely in hiragana. I'm guessing that the test proctor thought that it would be easier for test takers to understand if there were not any kanji. More likely, he didn't think about anything at all and just followed the instructions he was given, which were for students of all levels. Aside from the fact that I hadn't seen sentences in all hiragana in years, I think that this type of writing has always been a problem for me personally. This is how that sentence should actually look, in the version that includes kanji for every character:

携帯電話の電源を切って下さい。

That might seem overwhelming for those of you that are beginners, but it will become much easier than the all-hiragana version at some point in your studies. Also, the furigana version (when the readings of kanji are written on top of them) should be easier, too, once you've learned hiragana:

携帯電話(けいたいでんわ)の電源(でんげん)を切(き)って下(くだ)さい。

Japanese needs to have kanji, because it is vital for clarifying the meaning of written words. One example of this is homophones (words that sound the same). There are a ridiculous number of homophones in Japanese, and if everything were written in hiragana, then they would also become homonyms (words that are spelled the same), and no one would be able to understand anything.

For example, what if I had the following sentence, written in all hiragana:

きしゃがはやい

If we're talking to someone, we'd probably understand the meaning of this sentence simply based on the context of the conversation. But sometimes when reading, there is no context. And that's why kanji can be a lifesaver.

We have two words in this sentence, connected by the particle が / ga:

1. きしゃ
2. はやい

きしゃ / kisha could mean either 記者(きしゃ) (“reporter”) or 汽車(きしゃ) (“steam-powered train”).

はやい / hayai could mean either 早(はや)い (“early”) or 速(はや)い (“fast”).

So now we have all of these possibilities for kisha ga hayai:

記者(きしゃ)が早(はや)い = “The reporter is early.”

記者(きしゃ)が速(はや)い = “The reporter is fast.”

汽車(きしゃ)が早(はや)い = “The train is early.”

汽車(きしゃ)が速(はや)い = “The train is fast.”

Perhaps this is a bit of an extreme example, but I hope that it clarifies my point a bit. You might be worrying that this all sounds way too complicated, but it's not anything you have to worry about. Instead, it's something that you'll get used to naturally from focused exposure to the language. And as for the subtle differences between some kanji, don't fret about it. I have seen Japanese people mix up the kanji we just looked at, 早い and 速い on a number of occasions.

What this basically all comes down to is that written Japanese is the result of smashing a foreign writing system onto a completely different spoken language, and the results are, well, complicated. That said, studying this writing system, and the ways that it interacts with the language as a whole, can be a fascinating experience. It's not something to be afraid of. Instead, it's something to look at with enthusiasm and curiosity. We can get through this, I promise you.

Katakana, by the way, is basically just the same thing as hiragana, only it's used for foreign loan words, (usually foreign) people's names, and to add emphasis to words. So, for instance, some words that would use katakana are the names of cities around the globe, things that were recently invented in countries other than Japan, your name, etc.

Also, if there are any language nerds out there like myself that want to read up on homophones in Japanese a bit more, I thought that this article on KanjiClinic.com was quite an interesting read.