Example sentences
yīn因wèi为xià下yǔ雨，méi没qù去。
Didn't go because of rain.
yīn因wèi为máng忙，wàng忘le了。
Forgot because I was busy.
About this word
因 is cause, and 为 here is the 为 of 为了, meaning for or on account of. Two cause words joined make because, the standard introducer of a reason clause. Chinese keeps the pair 因为...所以... far more readily than English keeps because and so together, so 因为下雨，所以我没去 is perfectly normal, and dropping 所以 is equally fine. The word also takes a bare noun phrase (因为这件事, because of this matter). 由于 is the more formal equivalent.
The story behind the character
因
因 is 大 (a person) resting inside 囗 (a mat). A body lying down on something. Xu Shen wrote 因, 就也: to go along with, to lean on. From leaning on a mat you get a basis, then a reason, then "because." The mat is still there in the shape.
为
为 began as a hand on an elephant. The earliest forms show 爪 (a hand) above 象 (an elephant), and the usual reading is that people were putting elephants to work. Xu Shen, writing a thousand years later, guessed it was a monkey. 為, 母猴也, he wrote. He was wrong about this one. The elephant only turned up once scholars got a look at the oracle bones.