The printer, the inks, and the media have no intelligence in knowing how to accurately print an image. It is the relationship between the Rip and the Color Management that corrects the color. The Epson, Canon, HP drivers all are rips. They convert pixels and lines into dots per inch. They also control the printer to produce and accurate output.
How profiling works:
You are given a chart of colors by the Color Management Software that cover the color spectrum. These charts contain a relationship from light to dark colors very much like a linearization in a Rip. You print the chart without adding any profile to it, therefore; it has no correction or restructuring. Then, with a spectrophotometer, such as an i1 from Xrite, you read these colors into the software and it compares what color values of the patches it gave you and what it received in the printing and then it corrects for the differences as best as it can. Now, you might ask what does that mean? Do I need better software?
The ink set you are using, no matter what brand, only has a few color inks, unlike a painter that goes to his supplier and buys as many colors as he or she wishes. Therefore, given your basic CMYK or Hexachrome color pallet of your printer, the correction, the profile, will restructure the amount of each color necessary to make the best color correction it can. The media plays an important roll. The better the coating on the media, the higher the gamut of colors.
The Profiles Color Gamut:
There are billions of colors and depending on the media, you may only receive between 300 to 600 thousand colors. The main question you need to ask is, does the amount of colors I am obtaining, the colors I need or want. Am I obtaining good reds and other colors I need? Having a large color Gamut does not insure you getting the colors you need. It does, however, it give you more potential for reproducing a wider range that maybe what you need.
I am mentioning this aspect, because our company receives a number of calls and Emails from people looking for more color, richer reds, cleaner color, and many issues regarding color accuracy as well as color saturation.