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I was trying to build an OCR system and heard about ANNs. I am weak at mathematics and statistics and couldn't stick up to reading those massive mathematical documents (research papers or ANN related books). But I kind of figured out that ANN training is all about balancing of weights and biases. Am I right? And please also point me to some docs where I can get help understanding ANNs to use in my OCR system.

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Sorry, this is a very broad area. Proper understanding of neural networks requires advanced mathematics. It's not sufficient to say "balancing of weights and biases" because most ML algorithms have weights. You seriously need to grab a book.

OCR system itself is also very broad, it includes various object recognition techniques. You haven't even mentioned what you want to detect.

If you want to study, try:

https://github.com/Elucidation/tensorflow_chessbot

This is a well-documented OCR example for chess pieces. The project uses both regression and convolutional neural network.

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