Drebin Points (DP) are the currency earned in Metal Gear Solid 4: Guns of the Patriots used for purchasing weapons and upgrades in the game's pause menu via "Drebin's shop."
Drebin 893 made his living off the war economy. The points, as he put it, allowed him to put "the food on [his] table." He met Solid Snake and offered him a deal: in exchange for points Drebin would provide Snake with weapons and upgrades for his mission.
When the SOP through GW got hacked by Liquid Ocelot the war economy was stopped. As a result, it made it almost impossible for Drebin to earn money from the wars. But this did not faze Drebin as he provided his service, however small it was, to help Snake and Mei Ling's crew stop Liquid. As a result, Drebin's products were cheaper but the amount of Drebin Points earned decreased.
After the Patriots' AIs were destroyed and SOP along with them thanks to the FOXALIVE virus the war economy was depleted significantly to the point no one would be able to make a good sum of money. Otacon assumed that this means Drebin was out of work. Drebin, however, welcomed the Patriots' death due to the fact that the DREBINS no longer had to answer to them and they could set up their own business.
Drebin Points can be earned by collecting weapons, items and emblems and finding secrets. The amount of Drebin Points that are earned depends on the value of the weapon, as an RPG is worth 6000 Drebin Points, but a handgun would be worth very little in comparison.
The emblem with the highest amount of Drebin Points is emblem #1 "Big Boss" with the lowest being emblem #40 "Chicken." Listening to the flashbacks at Shadow Moses Island will earn a large amount of Drebin Points but if the player pauses or moves to the next flashback will not gain the Drebin Points.
The player cannot buy non-lethal weapons in the Boss Extreme difficulty, even if they have enough Drebin Points so as to not make it too easy to get the Big Boss emblem.
Behind the scenes
Drebin Points acted as a currency for Metal Gear Solid 4. Because it was the first time in the franchise to use a shop to buy equipment, several elements of Drebin Points and the Drebin Shop were tweaked, including the addition of discounts on Wednesdays and Sundays from 50% to 20%, to reduce the risk of players exploiting the system to come up with infinite ammunition, which was a great cause of concern for the staff during the leadup to launch. Fortunately, there weren't any recorded instances of players making any cheating attempts in the game.
Drebin Points also acted as the currency on the official site for Metal Gear Solid 4, which could be used to buy apps and wallpapers for the PlayStation 3.
Although Drebin Points themselves don't reappear in other Metal Gear games, their mechanics were reused in two other games: In Metal Gear Solid: Peace Walker, picking up any items that the player is unable to carry due to a full load will automatically be sent to Mother Base, similar to how picking up various ammunition or items that the player is no longer able to carry will be able to be sent to Drebin in Metal Gear Solid 4. In Metal Gear Rising: Revengeance, the reward system was redone with the Battle Points system, which could be earned by collecting holochips, or by defeating enemies. They can be used to purchase skills and upgrades for Raiden.
Even though the Drebin Points were a frequent game mechanic in Metal Gear Solid 4, they were never given a physical depiction in-game. The closest they have come to receiving an actual physical appearance is in one of Little Gray's cards for the Droid/iPhone app Metal Gear Solid: Social Ops.