When both players are currently not committed to anything. Neither player is in mid-attack, neither player is in range of another player, no one is currently rolling, etc.
Basically, from the neutral stance (also know as neutral position, or simply "the neutral"), all players have access to all of their options. It's important to recognize the neutral, as well as know what your character can do to take control of the neutral and put yourself into an advantage. For example, in the neutral, Diddy is likely to throw a banana, Villager will likely plant a sapling, Mega Man will likely throw a blade into the ground to pick up. Other characters will try to take advantage of the neutral with mixups, like Sheik air tossing needles and doing a bouncing fish to catch a potential spot dodge, or Bowser doing a jump-in klaw to bait a shield and punish it.
Some characters excel at never giving the opponent to neutral, like the spacies and Sonic. They're fast, or have a quick, safe projectile that doesn't let your opponent get any breathing room. Other characters rely on resetting to the neutral, like Shulk, who uses long hitboxes from a safe distance to deter opponents long enough to switch his Monado Arts.
Different characters use the neutral in different ways, and it's one of the keys to improving at any competitive game.
