Question: Genesis 2:10 mentions a river that flows out of Eden to water the garden. Does this mean that Eden was more than just a garden? Could it have been a larger region that had a garden in it?
The geographic details on Eden are found in Genesis 2:8-14. There are several details in the description that give us a general idea of Eden’s size and location. It must be remembered, however, that the geography described here is from the pre-Flood world. The Flood itself, and other calamities in nature associated with the Flood—earthquakes, volcanoes, tsunamis, etc.—dramatically changed the landscape of the earth. It is impossible to accurately locate exactly where Eden was or how large an area it took up based on the descriptions in Genesis 2 because the landmarks have all changed.
That being said, there are some things we can discover. Eden lies “east” of the point of view of Adam, the one who first passed on this description. We don’t know where Adam was at the time Eden and the garden were created, or if Adam’s point of view reflects where he was when he was telling his children about the creation of the garden. It could be assumed that Adam was somewhere in the area of what we now know as Palestine, based upon a further assumption that the Tigris and Euphrates rivers mentioned in the account might be somewhat close to where these rivers were located before the Flood.
The garden, as the questioner suggests, was actually “in Eden” (2:8) and the river that fed the garden originated from an underground source somewhere “from Eden” into the garden (2:10). This river had to be quite large because it separated into four other large rivers after feeding the garden (2:10).
Adam named the first river “Pishon,” which he described as winding through, or perhaps encircling, the land of Havilah. Havilah ceased to exist after the Flood, so we don’t know where it was located. The name seems to mean “Sandland,” and it was known for its wealth of gold, precious stones and an aromatic gum (2:11-12).
Adam named the second river Gihon (2:13). That river circulated through the land of Cush. Later in Scripture, Cush is the name given to Arabia and Ethiopia. It is possible that the same general area was renamed Cush after the Flood, even though the natural boundaries had changed dramatically.
Adam named the third river the Tigris, or “Hiddekel” in Hebrew. The Tigris is described as running along the eastern border of Assyria, which in post-Flood times would be north / northeast of Arabia.
The last river is the Euphrates, and no description is given of its location. If the Tigris and Euphrates of Adam’s pre-Flood world are reasonably close to their current locations, then the Eden of the Bible would extend roughly from the modern day Persian Gulf northward to encompass Iraq, western Turkey and the stretch of northwestern Iran between Turkey and the Caspian Sea. The garden in Eden would be a smaller area tucked somewhere near the headwaters of the original rivers.