The fight with two weapons in D & D 5th Edition requires that
- Take the "Attack Action" during your turn, and
- When you use that action, use a Light weapon, that if these two restrictions are met, it allows
- Use a Bonus action to make an additional "weapon attack" using the other weapon in the other hand, as long as the other weapon is also Light.
So as a level 1 fighter, you would make 2 attack rolls, one for the Normal Action, one for the Bonus Action. As a level 5 fighter, you would make 3 attack rolls, 2 for Normal Action, one for Bonus Action; in level 11, 4 rolls (3 regular, 1 bonus); at level 20, 5 rolls (4 regular, 1 bonus).
Making multiple attack rolls, one for each attack, makes it more likely that at least one of your attacks will connect; Consider, for example, a level 4 fighter who makes 2 attack rolls with this feature. If they have been optimizing the damage output, they will have a Strength score of 18, which makes their modifier STR +4. So his + HIT will be +6, and the damage modifier in his weapon attacks will be +4.
Against an AC16 target, they will have a 55% chance to hit the target, as they must roll a 10 or more on their d20 roll to hit successfully. But because they make two attacks, each attack has its own 55% chance of hitting, so the probability that at least one of the rolls is (1- (1-.55) ^ 2) == 0.7975, or a probability of 79.75%. .
So, instead of hitting about half the time in combat, you will successfully get 4/5 times in each round when you make individual attack rolls.
Keep in mind that this does not affect your average damage; your DPR (Damage Per Round) As a level 4 Champion with 18 strength and two short swords against an AC16 target is 8.95DPR, regardless of whether you make two attack rolls, or make an attack roll and use the result for both attacks.
So, if your DM was considering adopting a variant rule in which he combined his attack rolls in a single roll for all attacks, I would advise against doing so. it does not improve your average damage, and makes individual rounds of combat less satisfying.