A neutral attack (officially standard attack, jab, and weak attack/弱攻撃, also known as a neutral A, neutral combo or AAA) is an attack performed by pressing the attack button, the A button by default, while one's character is standing, and the control stick or d-pad is in a neutral position. A neutral attack can also be performed by crouching and tilting the Control Stick diagonally downwards in the opposite direction the character is facing, as well as by pressing the grab button right after returning to the standing animation after crouching. Jabs are typically fast, short-ranged, weak hits that are useful for starting combos, or to escape from close-range pressure. Many jabs, such as Mario's, form natural combos of two or three hits, the final hit usually inflicting the most damage and knockback, while others, such as Fox's, initiate rapid, continuous, multi-hit attacks that opponents must often DI out of. As of Super Smash Bros. 4, said rapid jabs (also known as a "neutral infinite"; officially known as a flurry attack in English and either a barrage attack/連打攻撃 or hundred rending attack/百裂攻撃 in Japanese) end with a powerful hit (dubbed as the hundred rending finish/百裂フィニッシュ in Japanese) instead of simply cutting off once the player stops pressing the button, which makes them safer to use at the expense of now having slightly higher ending lag.
The speed at which each hit in the sequence of a neutral combo is executed can be controlled through the timing of a player's button taps. In Melee and Brawl, neutral combos may be interrupted by crouching or shielding, in order to restart them, or to perform other moves quickly after canceling them.
Despite their intended use, most neutral attacks have a long duration and moderate ending lag, making them very punishable if whiffed. The hits can also be smash DI'ed out of, have poor range, and most are inferior to other ground attacks a character may have, such as forward tilts and down tilts. Prior to SSB4, rapid jabs in particular have disproportionately high ending lag to their non-existent knockback, can be easily punished, and cannot be ended easily, because tapping the attack button to perform something else only extends the time the rapid jab is held.
In the original Super Smash Bros, standard attacks consisting of consecutive hits, which form neutral combos, are executed by tapping A the appropriate number of times. Characters who possess a rapid jab are able to repeat it steadily and indefinitely if a player repeatedly taps A once the rapid jab is initiated.
Similarly to the original Smash Bros, in Melee, standard attacks that form neutral combos are executed by tapping A the appropriate number of times, and characters who possess a rapid jab are able to repeat it steadily and indefinitely if a player repeatedly taps A once the rapid jab is initiated. Many CPUs use this attack often.
In Brawl, holding the A button has several uses when performing neutral attacks. Standard attacks consisting of consecutive hits that form neutral combos may be executed either by tapping A the appropriate number of times, or by holding A when one of the attacks connects with an opponent. Characters who possess a rapid jab are able to repeat it steadily and indefinitely if a player holds A once the rapid jab is initiated, however, tapping A repeatedly also works. Additionally, if A is held without attacking an opponent, some characters are able to repeat the first hit of their jab continuously until it does connect, after which their neutral combo will follow, a technique called consecutive jabbing. It should be noted that different characters' consecutive jabs repeat at different paces, with Fox and Snake possessing very fast consecutive jabs, and Ike and Sonic very slow ones. 
*Meta Knight's neutral attack is unique, as it is the only jab that functions as a rapid attack, but cannot function as a single hit attack. When A is pressed, a rapid attack is immediately launched and may be continued indefinitely. However, even if A is not held, Meta Knight will slash several times before the move ends.
**Pit's neutral attack can function as either a three hit combo, or a two hit combo that launches into a rapid attack, depending on the player's input. If A is held during the second hit, Pit performs the three hit combo, but if A is pressed three times, the rapid attack initiates and continues for as long as A is held afterwards. Pit is the only character who possesses two different types of jabs.
All rapid jabs, with the exception of the Villager, now end with a stronger finishing hit that launches the opponent away from them after enough time in the jab. These finishers have slightly longer range than rapid jabs, allowing the attacker to safely end the move and knock away opponents if they escape. The attacker will also be gradually pushed backwards as they land more hits. All this serves a dual purpose, to both remove infinite combos and give jabbing fighters the ability to knock their opponent away when they are done with them. Additionally, rapid jabs themselves seem to have been sped up.
* This assumes the Mii is default height and weight.
Super Smash Bros. for Wii U digital manual description
"Press to perform a standard attack. Press repeatedly to perform a series of attacks. With some fighters, you can hold to attack continuously until you hit an opponent. You'll then automatically unleash a series of standard attacks."