The Japanese writing

In the Japanese language there are three forms of writing. The first was the Kanji (ideograms), which came through the Chinese, but the Chinese is used many ideograms, so only the most frequently remained in Japan.
Kanji had many ideograms, then created the hiragana for women who don't have access to education could write, and finally, the katakana was created by Buddhist monks. Over time, the three alphabets started to be used together, each with their function.  

Kanji  
They are ideograms where each symbol can represent a word, na idea, a concept or na object may have, sometimes more than one way to pronounce / reading.  In Kanji there are more than two thousand ideograms, but has the most frequent, called Jouyou Kanji, which is a list with 1945 kanji established by the Ministry of Japanese Education.
1006 kanji Japanese learn at primary education, note:  

And the other 939 kanji they learn in secondary education.  

Hiragana
Main alphabet Japananese language. Hiragana is used to write native word of Japan, all Japanese words that have no kanji, are written in hiragana. The hiragana has 46 letters can sometimes be modified.  

Katakana
It's the alphabet used to write foreign words, for example foreign names, country names and more... and It's also used to write onomatopoeia. It's easy to understand it when you already know the hiragana, because they both work the same way. The katakana also has 46 letters and they can also be modified (The letters are modified in the same way in hiragana nand katakana).  

And finally...  

Romaji
The romaji is basically the sound representation of Japanese words with our alphabet. Note the example:
Japanese: 日本語を勉強しましょう (let's learn Japanese)
Romaji: Nihongo wo benkyou shimashou