I'm a beginner at Japanese, recognizing less than 100 of the kanji, but I can already vouch for them.
In text constisting of latin alphabets, spaces are important. They provide anchors for the eyes to locate and to estimate the length of the current word. When reading text, the eyes jump from a word to the next, using the spaces as a hint.
In Japanese text, there are no spaces. I will now show how that works. Here is a sample of Japanese text.
Observation 1: all of the symbols in the text are the same width. They are all in a nice grid (except for the line containing the western "2" digit). Because most of the Japanese words are quite short, it makes it easy for the brain to estimate where the next word begins in the text.
I have underlined the first three words from this sample text. It is easy for me to do, because the words are written partially using kanji.
Kanji are easy to spot, even if you don't understand them. The kanji act as anchors in the text - when you see a kanji, it'll almost always begin a word. It acts as an anchor, similar to spaces in English text. Had the text written in hiragana, it would be (sorry, no image this time):
いつもたのしくみてますが
can you figure out where a word ends and the next begins now? It's certainly a lot more difficult.
The human brain is very effecient in recognizing images. It is why we can read so fast. Kanji-using writing systems benefit from this a lot. When the reader sees the symbol "見", he can know immediately it is something about
seeing, even before he has read the rest of the word. If it is written with the syllable "み" (mi), he has to guess from a lot more options and can only understand it when he has read the rest of the word. For this reason, the kanji make the text faster to read, once you are proficient enough to recognize the kanji.
Incidentally, kanji have also a compression effect. In this example, the word "tanoshiku" (four syllables: ta no shi ku) is written using the kanji for "tanoshii": it is now broken into kanji TANO and the syllables shi ku. This makes three symbols, one less than if it had been written in hiragana only. This lowers the subconscious search time for the next word, and makes it faster to read.
たのしく became
楽しく
Japanese verbs are inflected. Due to the inflections, there are some word endings that occur from time to time. In this example, the third word reads as "mitemasuga,". The "masu" ending (ます) occurs very frequently in polite Japanese text, and it is usually the first thing beginner Japanese learners will be able to read. Since it always occurs in the end of the word and it's easy to spot, it makes up for an anchor (see the beginning of this post). The "ga," in this word is actually a particle meaning "but," or "because,".
And yes, the kanji are very essential in differentiating words that are otherwise pronounced the same way.
kami = 神 = god.
kami = 紙 = paper.
kami = 髪 = hair.
Like I said earlier, readers who recognize these kanji will understand the meaning from kanji much faster than from the hiragana. This is why they are used. And because they're shorter than " かみ" (kami). Even without the kanji, the readers could understand the meaning from the context, exactly like in speech. But kanji just makes it faster to read.
Only when the word is written separately without context, a kanji is necessary.