I saw the word 'fathom.'
In my language, it has same meaning as 'understand.'
Is it really same? What is the difference between fathom and understand?
There are (almost) no sets of words in any language that mean exactly the same in all circumstances. If such a thing happens, usually one word stops being used.
The verb fathom is a nice one. If we look at etymonline.com, we find this:
Old English fæðmian "to embrace, surround, envelop;" see fathom (n.). The meaning "take soundings" is from c.1600; its figurative sense of "get to the bottom of, understand" is 1620s. Related: Fathomed; fathoming.
I know the related word vadem in my native Dutch as relating to measuring the depth of water under a ship. This is the "take soundings" meaning in the etymonline text. Taking soundings is a way to measure the depth of water.
From that depth of water (you have to get to the bottom to measure that depth, with sound or with a stick), the meaning "get to the bottom of something" evolved.
In a way, that means "to understand something", but the implication is that you are talking about something reasonably complicated, that needs some work to understand.
You can say that you fathom the implications of the General Theory of Relativity (although many would doubt you are right), but if I tell you that you should look before crossing the street, you would not "fathom" that.
So if you mean understand in the sense of getting to the bottom of a complex problem, it means the same as fathom. But understand as in "do you understand what I said?" or "I don't understand this question" cannot be replaced by fathom.
Laure mentions two other expressions in the comment and I think they are great to compare with.
In the sense of getting to the bottom of something, figuring something out is a good alternative to fathom.
In the sense of probing (what etymonline mentions as the literal taking soundings), estimating also is a possible meaning of fathom:
I could not fathom the depth of his hate.
In that sentence, fathom implies indeed that I can not estimate that depth. I could again use understand here, but it would not convey the (exact) same meaning.
So, use fathom when there is a definite sense of a process involving estimating something or figuring something out, or coming to understand something. Generally, do not use it when you describe the (static) situation of "having understanding of something".
Overall, do not use it too often anyway, because it has an antiquated feel to it for many people. Fathoming the depth of an emotion I would almost see as a fixed expression by now, and it works well because of the link to "measuring depth".