Magnitude essentially just means large size, but it could be used metaphoricallly to means such things as "He didn't realize the importance of" or "He didn't realize the possible ramifications of" or "He didn't realize all the implications of" or "He didn't realize the extent of" or "He didn't realizes the complexities of." A typical example would be "He didn't realize the magnitude of the problem." He thought it was a simple problem or a simple task, but he did come to realize as he became more involved in it that it was far more complicated than it had appeared to him at first sight. He thought there was an easy answer, but his answer just evoked another question, and the answer to that question evoked another question.
If you use a good collegiate dictionary you can usually find the simple origins of complex words at the end of the definition. Magnitude come from the Latin magnitudo, derived from magnus, meaning great.
He didn't understand the importance of (something).