The purpose is to kind of offset the fact that a minor injury causes a seeping wound that matches a bullet wound. A small wound would incur very minimal bleeding, whereas a bullet wound would cause near the current level of bleed, and a heavy bleed can be in place for multiple bullet wounds, very close explosives, or combined wounds.
As for how it would be implemented in game, each stage would just add a specific amount of bleed for that respective level, creating the illusion that the bleeding is getting worsened. (At level 1 bleeding, a small bleed effect will be applied. At level 2, that same effect may be applied 'over' the level 1 bleed, so that he is now bleeding at twice the rate)
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Stage 0 Bleed: From 100% health to the current bleed level, no bleeding would occur.
Stage 1 Bleed: From the current bleed level to X% of health, stage 1 bleeding will occur; the 'bleeding' screen effect would be minimal, or less intrusive than the current screen, and the rate of bleed will be very low. Stage 1 bleeding will most likely occur when the player takes minor fall damage, or is in the very edge of radius of an explosive, etc.
Stage 2 Bleed: From X% health to Y% health, stage 2 bleeding would occur, which should be the average damage of a bullet hitting the player. This could be the current bleed effect, or a small bit slower, depending.
Stage 3 Bleed: From Y% health to Z% health, stage 3 bleeding would occur which would be nearing the black-white phase where it will be critical to heal the player before they become critical.There could be an 'unlimited' amount of bleed stages.
For instance: from 99% to the current bleed effect a very very low bleed could be present, that would try to be as minimal as possible, just to let the player know they aren't at full health, and should look into getting healed soon. It could probably even be made so that there is no actual bleeding occuring, but a non-invasive screen effect (say, a reddened ring on the edge of the screen) was overlayed to give a sense that he's still hurt a little, but doesn't need to be immediately healed.
Or, instead of having just 3 levels of bleeding, you could separate them further to create a very intuitive bleed system; for instance, you could have a bleed level that includes the damage ranges caused by a 5.56 NATO round, and also have a higher bleed level for damage caused by 7.62 rounds, to give another slight advantage to having the larger round.
(Please, before posting, realize that any amounts of bleed I mention or imply here are simply 'options', please focus on discussing the idea, and perhaps different 'levels' of bleed that could be added, but there's no need to nitpick the levels of bleed I have posted as they are purely for example)