I checked up the BDB lexicon and some softwares to study the usage of the word אֲשֶׁר in Bible. However in my level its seem so complex and I am unable to understand properly. Can anyone please tell me in simple words how and when this word "אֲשֶׁר" is used in Biblical Hebrew?
This word simply is the equivalent of the relative pronoun in English—it means "which" if referring to an object, place, or thing, and "who" if referring to a person. It simply serves to identify or describe the person by something which characterizes them.
So, for example, Genesis 3:17:
And He said to Adam: Because you have harkened to the voice of your wife, and have eaten of the tree about which [אשר] I gave you instruction, saying that you shall not eat of it, the ground shall be cursed for your sake: you shall eat of it in grief all the days of your life.
Here it serves to specify the tree: this is the tree of the knowledge of good and evil, about which God gave instruction ("You shall not eat of it").
Again, Genesis 1:7:
And God made the expanse, and separated the waters that were [אשר] under the expanse, from those [אשר] above the expanse: and it was so.
Even though the letters א, ש, and ר are used in other words and names, it should not be confused for this word.
Unless I'm missing something, this is in the BDB and should answer your Question?
H834 אשׁר 'ăsher BDB Definition: 1) (relative participle) 1a) which, who 1b) that which 2) (conjunction) 2a) that (in object clause) 2b) when 2c) since 2d) as 2e) conditional if Part of Speech: relative particle conjunction A Related Word by BDB/Strong’s Number: a primitive relative pronoun (of every gender and number)
Furthermore, you can see the first citation of אשׁר in:
Gen 1:7 ויעשׂ אלהים את־הרקיע ויבדל בין המים אשׁר מתחת לרקיע ובין המים אשׁר מעל לרקיע ויהי־כן׃
KJV Gen 1:7 And God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament: and it was so.
אשׁר is a general part of Hebrew speech, nothing to in-depth.