In one line
If someone saw three ads before converting, whose win is it? Attribution is the rule that answers that — how credit for a conversion that already happened gets assigned across touchpoints.
It is a rule, not a fact
This is the part that matters most. Someone sees an Instagram ad, clicks a search ad days later, then installs. Whose install is it?
There is no correct answer. So you pick a rule: give it all to the last click, split it across touchpoints, or count only touchpoints inside a set window.
Attribution numbers are the output of that rule, not a law of nature. Change the rule and the numbers change.
Do not confuse it with incrementality
Attribution asks "who should we record this conversion under?" Incrementality asks "would this conversion have happened without the ad?"
Completely different questions. Attribution always allocates 100% somewhere, while real incremental effect can be far smaller than that total. Brand search advertising is the clearest example — attribution credits it heavily, yet many of those users would have arrived anyway.
Why systems disagree
Conversion counts differing across the ad platform, GA4 and your MMP is not a malfunction. Their attribution windows, processing times and conversion definitions differ.
Before picking which number is right, put each system's rules side by side. Most "data errors" are explained there.
Go deeper
How to narrow down mismatched numbers across systems is covered in attribution data mismatch; why attribution cannot establish causality is covered in correlation vs causation.