There are many explanations of the intent of his divisions. Here is one:
The Maharal points out that the plagues follow a pattern, split into units of 3 - the first of each group (plagues 1, 4, and 7) are preceded by a warning to Pharaoh issued by the Nile. The second of each group (2, 5, and 8) are preceded by a warning issued to Pharaoh while sitting on his throne. The third of each group has no warning.
The Maharal explains that the plagues are in 3 groups, working their way up through creation, and each group within itself increases in intensity. The first group is in the earth itself - water to blood, frogs from the water, and the dust being turned into lice. The first had its warning by the Nile, outside of Pharaoh's seat of power. The second was closer to home, with the warning at the throne itself. The third did not even get a warning.
The second group is on the land - plagues against man and animals, again with the same progression of intensity.
The third group is the sky - hail which came from the sky, locusts which blocked out the heavenly bodies, and darkness which completely blocked out the light of the sun, with the same progression.
The plagues were split into these groups of three to split them into their divisions of which part of existence they targeted.
The final plague was a "grand finale" which also did not get a warning, but was the culmination of the entire display.