The two-armed fights in the 5th edition of D & D require you to:
- Take "attack action" during your turn, and
- When you use this action, use a Light weapon that, if these two constraints are met, allows you to
- Use a Bonus Action make an additional "weapon attack" using the other weapon in the other hand, provided that this weapon is also Light.
So, as a Level 1 fighter, you would make 2 attack rolls, one for Normal Action, one for Bonus Action. As a Level 5 fighter, you would make 3 attack rolls, 2 for normal action and one for bonus action. at level 11, 4 throws (3 regulars, 1 bonus); at level 20, 5 reels (4 regular, 1 bonus).
Making multiple attack rolls, one for each attack, increases the probability that at least one your attacks will connect; consider, for example, a Level 4 fighter performing 2 attack rolls with this feature. If they optimize their damage, they will have a strength score of 18, which will give them a STR modifier of +4. Thus, their HIT will be +6 and the damage modifier of their weapon attacks will be +4.
Against an AC16 target, they will have a 55% chance to hit the target, as they will need to roll a 10 or more on their d20 roll to hit. But as they make two attacks, each attack has a 55% chance to hit, and so the probability that at least one throw is hit is (1- (1-55) ^ 2) == 0.7975, which is 79.75% chance. .
Thus, instead of hitting about half the time in combat, you will be able to hit 4/5 times per round when you make individual attack rolls.
Note that this does not affect your average damage; your CMA (Damage per turn) as a level 4 fighter with a strength of 18 and two short swords against an AC16 target worth 8.95DPR, whether you make two attack throws or an attack roll and use the result for both attacks.
So, if your DM was considering adopting a rule variant in which you combined your attack rolls into one for all attacks, I would advise against it; this does not improve your average damage and makes individual combat rounds less satisfying.