Plinking
Plinking (sometimes pronounced "P-Linking") stands for "Priority Linking" and is a fundamental technique to getting the most out of your combos. It makes difficult combos much easier to achieve.
The Technique
Plinking is done by dancing across two or more buttons in rapid succession exactly one-sixtieth (1/60) of a second, or one frame, apart. It sounds a lot harder than it really is. However, it is typically very difficult to perform on controllers apart from an arcade stick because of the button layout and design on most pads (i.e. standard Xbox 360/PS3 controller). The catch is that it only works if a higher priority command is input first.
The Mechanics
This technique exploits a mechanic in SSF4 that gives certain commands priority over others. The formula is relatively simple: medium attacks have priority over light attacks, heavy/hard attacks have priority over both, and kicks have priority over punches. The priority list looks like this:
LP<LK<MP<MK<HP<HK
By exploiting this using plinking you get an extra frame to hit the next move in your combo, which makes the notorious one-frame links entirely possible. There are two reasons to use plinking over attempting to hammer the same button twice within 2/60's of a second. One, it is almost physically impossible to do so. Two, if you tap the same button that rapidly, the game thinks that the button is being held down and ignores the second input. Plinking essentially jars the system by adding another input and allows the system to register the second input of the higher priority command. It's possible the second input of the first command is due to negative edge, but this is currently unverified. When done successfully the inputs should appear like this: 
Notice how the first input is registered twice? This is what adds that extra frame to the one-frame window used in many difficult links. Because of the priority system, the lesser input (MP) is ignored in favor of the higher input (HP). This principle applies to any input and any combination of inputs, allowing for a large amount of plinking possibilities. However, you can only plink a light kick to a light punch when crouching, but you cannot plink MK+MP or HK+HP without getting a focus attack or taunt, respectively. Light punch has priority over nothing, so it cannot be plinked.
Double Plinking
This technique is a plink that utilizes three buttons instead of two. It helps make a plink successful if the timing of the first input was a little off. It does not give an extra frame, it simply increases the plink's chance of succeeding. This is because it acts like you plinked twice.
True Double Plinking
The difference between regular double plinking and "true" double plinking is true double plinking actually involves two different plinks in rapid succession. This further increases your chances of hitting the one-frame link. It acts somewhat like an option select, but depends on your timing rather than the opponent's response. An example of this would be adding a MP+LK plink to a HP+LP plink. If you somehow miss the timing on the first plink (HP+LP) the second plink (MP+LK) will come out. This can be useful if you're having trouble with certain links.
Blinking/Slinking
This bizarre plink involves the use of the Back (Xbox 360) or Select (PS3) button, thus Blinking or Slinking. This is the only plink which is generally easier on a pad than an arcade stick (depending on the button layout). The Back/Select button is secretly the lowest priority input in the game, effectively having priority over nothing. Its usefulness is derived from its unique ability to double any input or any combination of inputs, giving an extra frame to each and can essentially plink the combination rather than the individual inputs. This includes light punch (which was previously impossible to plink), grab/throw, and ultras (3-punch/3-kick buttons). Focus attacks not yet confirmed. This is very useful for trying to do strictly timed throws, or even kara throws, ultras, and anything else. However, this is not possible for 3DS users, since the Select button acts as a second Start button. The slink will register and come out if done correctly, but at the cost of momentarily pausing the game. It is therefore not a reliable way to practice the technique, nor is it good to use in online matches.