Thank you for the interpretative question, “Why do we have verses 10–14 in Genesis Chapter 2?”
As one reads the broader context of Genesis 2:8–15, the text gives the answers. The text says this, “Now the LORD God had planted a garden in the east, in Eden; and there he put the man he had formed. 9 The LORD God made all kinds of trees grow out of the ground—trees that were pleasing to the eye and good for food. 10 In the middle of the garden were the tree of life and the tree of the knowledge of good and evil. A river watering the garden flowed from Eden; from there it was separated into four headwaters. 11 The name of the first is the Pishon; it winds through the entire land of Havilah, where there is gold. 12 (The gold of that land is good; aromatic resin[d] and onyx are also there.) 13 The name of the second river is the Gihon; it winds through the entire land of Cush.[e] 14 The name of the third river is the Tigris; it runs along the east side of Ashur. And the fourth river is the Euphrates. 15 The LORD God took the man and put him in the Garden of Eden to work it and take care of it” (A searchable online Bible in over 150 versions and 50 languages).
As one reads the text without verses 10–14, the obvious question is this, “Where is the Garden of Eden.” If God made the Garden, then why doesn’t God give us the location of it or maybe there is no Garden. The stating of the location shows that the Garden is a real place and not a fantasy. Two of the four rivers are not in question, Tigris and Euphrate River so it is likely that the two unknown river, Pishon and Gihon.
SUMMARY: Genesis 2:10–14 is given to show that the Garden of Eden is a genuine place with a specific location.
For more perspectives:
https://www.quora.com/Why-do-we-have-verses-10-14-in-Genesis-Chapter-2