It is probably somewhat inaccurate to say that the Nile allowed Egypt to have “agricultural growth.” That implies that Egypt could have had serious agriculture regardless and that the Nile simply helped Egypt’s agriculture to grow. It is more accurate to say that agriculture in Egypt was only possible on any sort of a large scale because of the Nile River.
The vast majority of the land area of Egypt is desert. This was what the ancient Egyptians called the “red land.” This land was completely useless for agriculture, largely because it could not be irrigated. By contrast, the area near the Nile (for a few miles on either side of the river’s normal banks) was very fertile. There were two reasons for this. First, the area was fertile because it was near to the water. Second, and perhaps more importantly, it was fertile because the Nile’s floods continually brought new soil and deposited it in that area. The Nile would flood, carrying huge amounts of silt. As the floods receded, that silt would be deposited. This made the “black land” near the river that could support intensive agriculture.
In that way, it was the Nile that made large-scale agriculture in Egypt possible.