Every attack uses its own Attack Roll, unless a feature specifically tells you otherwise
Two-weapon fighting in D&D 5th Edition requires you to
- Take the "Attack Action" during your turn, and
- When using that action, use a Light weapon, which if these two constraints are satisfied, allows you to
- Use a Bonus Action to make one more additional "weapon attack" using the other weapon in the other hand, provided that other weapon is also Light.
So as a level 1 Fighter, you would make 2 attack rolls, one for the regular Action, one for the Bonus Action. As a level 5 fighter, you'd make 3 attack rolls, 2 for the regular Action, one for the Bonus Action; at level 11, 4 rolls (3 regular, 1 bonus); at level 20, 5 rolls (4 regular, 1 bonus).
Combining all your attacks into a single attack roll doesn't affect your DPR, but will make your damage output less consistent
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 making 2 attack rolls with this feature. If they've been optimizing for damage output, they'll have a Strength score of 18, making their STR modifier +4. So their +HIT will be a +6, and the damage modifier on their weapon attacks will be +4.
Against an AC16 target, they'll have a 55% chance to hit the target, because they'll be required to roll a 10 or higher on their d20 roll to successfully hit. But because they make two attacks, each attack has its own 55% chance of hitting, and so the chances that at least one roll hits is (1-(1-.55)^2)==0.7975, or a 79.75% chance.
So instead of hitting about half the time in combat, you'll successfully land hits 4/5 times each round when you make individual attack rolls.
Note that this does not affect your average damage; your DPR (Damage Per Round) as a Level 4 Champion Fighter with 18 Strength and two Short Swords against an AC16 target is 8.95DPR, regardless of whether you make two attack rolls, or make one attack roll and use the result for both attacks.
So if your DM were considering adopting a variant rule where you did combine your attack rolls into a single roll for all attacks, I'd advise against it; it doesn't improve your average damage, and makes individual rounds of combat less satisfying.