Simplified example:
Persons A and B check out master branch.
Person A adds a.txt, commits and pushes.
Person B adds b.txt, commits and tries to push and...
1) git will not accept the push because it's not on top of current master branch, person B needs to fetch and merge/rebase before pushing again.
2) pijul will accept the change (after a pull, but no rebase) because patches A and B are independent of each other and does not matter which order they are in the history (keyword: commutation).
The value of Pijul will only start to show when you get into big three way merge scenarios. Which git users avoid like the plague because they are so nasty to deal with. Demonstrating this would need a much larger example.
edit: clarification a pull is still needed in case 2, but no rebase or merge because there isn't one for commutative patches