In doubles, good players can easily cover he whole court, much easier than in singles, where a single person has to cover an only slightly smaller area. To win a rally against a good doubles pair, you need to pressure them with fast downwards shots, forcing them to make a mistake.
To be able to play downwards, you need to force the opponents to play upwards, typically by playing shots to where they are not at the moment, so that they have to take the shuttle late. In this situation (taking the shuttle late, often just above the floor), playing short to the net would allow you to kill the shuttle immediately, so the least-worst option for your opponents is to play a high lift to the very back of the court.
So whoever wins this fight for the lift will have an advantage, but they have not won the rally yet.
When you are smashing the shuttle downwards from the back of the court, your partner should cover the front. This prevents your opponents from simply blocking the shuttle to the net, which would require you to lift.
Concurrently, your opponents have to optimize their positioning to defend against your smash. A good smash is way too fast to intercept near the net, so they will stand side-by side at about the middle of the court, so that they can get to any smash immediately without having to step. The direction where the smash would fly the shortest distance is the most dangerous, so the player on the side of the shuttle will typically cover less space. Other considerations such as relative defensive skills, handedness and speed may also affect the defenders' positioning, but it will always be side-by-side.
In summary, typical positions of attackers and defenders look like:
The defenders can play high lifts to the back of the court again, but in order for them to win, they are trying to get into the attack themselves.
This, finally, is where rotation comes into play: By playing to where the attackers aren't, i.e. between the attacking players, to the sides at the net, or flat shots to a side of the rearcourt, the defenders force the attackers to move around the court.
When the defenders find a hole in the attack, the attackers may have to lift the shuttle themselves, and now become the attackers. Both sides then have to reposition to the then-optimal positions.
Because a doubles player will roughly speaking always cover the opposite half of the court to where their partner is, this repositioning is called rotation.
To get a better feel for doubles strategy in general and the rotation it entails, watch high-level doubles matches.