Fathom (verb)

1. To understand the nature or meaning of something.
2. To grasp the essence or significance of something.
3. To comprehend the full extent of something.
4. To gain insight into the complexity of something.
5. To unravel or solve a complex problem or mystery.

Origin:

From the old english word fæþm, meaning 'the outstretched arms, an embrace'.

Examples:

1. She could not fathom the reason for his sudden departure.
2. He could not fathom how someone could be so cruel.
3. The complexity of the system was beyond his ability to fathom.
4. The solution to the puzzle was beyond his ability to fathom.
5. Despite his best efforts, he was unable to fathom the depth of the conspiracy.