Traits are a unique feature that a character has that is not universal. These vary depending on character. Some characters may not have any sort of traits, but that is usually made up by being strong in the basic facets of the game. Some characters also may have multiple traits, but opposite to the ones with no traits, they may be weaker on the basic mechanics side. Some characters may share traits, but they are generally unique to each character.
These are all the traits that a character can have:
Chain Combos: The Chain Combo trait will allow the player to chain normal attacks into stronger normal attacks. You can chain light normals into medium normals, and medium normals into heavy normals. You can also go from light to heavy as well. When chaining attacks, you cannot chain a punch into a kick with the same strength more than once in a combo (i.e. you can't do MK > MP > MK, but you can do MK > MP > HK). You also cannot chain heavier attacks into lighter ones.
Air Combos: The Air Combo trait is similar to the Chain Combo trait. You are able to chain air attacks into one another, and some aerial attacks will cause a "spike" knockdown, which is used to end the air combo. Characters with air combos will also generally have a launcher attack, so they can properly combo into their air combos on the ground.
Jump Cancels: The Jump Cancel trait allows the player to cancel certain buttons into their jump. If they also have the Air Jump trait, then they are able to jump cancel some air normals as well, making their movement very strong, while lowering their commitment to air attacks. Generally, this trait is reserved for rushdown characters, or hit-and-run characters.
Dash Attacks: The Dash Attack trait changes the behavior of some normals on the character. This is also available to the Dynamic type, despite the name. The actual changes vary depending on character, but dash attacks can change the frame data, animation, and even movement speed of the given attack.
Air Jump: The Air Jump trait allows the player to jump in the air. This essentially means that the player has access to a double jump, however the air jump doesn't have a short hop or super jump variation like the ground jump does. You are also only allowed to air jump off of a normal or super jump, and not a short hop or hyper hop. This can give way to many different mix-ups and interactions that would otherwise not be present.
Super Armor: The Super Armor Trait turns the character into an unstoppable wall. They are able to absorb hits on a lot of their attacks, and depending on character, they don't even need to attack to have the armor. Depending on the character, the armor may negate damage entirely, or take damage, but be unphased by the attack itself. Generally, characters with Super Armor that is active while in idle actions will take damage from attacks but not reel back from the attack whatsoever, whereas characters who have armor only on some of their attacks negate the damage they sustain from an attack and do not reel back.