Robert's Rules for Postponing a Motion Indefinitely
The subsidiary motion to postpone indefinitely is the Robert's Rules way of avoiding uncomfortable decisions; its adoption means that your group has agreed not to decide. The adoption of postpone indefinitely says it's better not to decide than to decide one way or the other. It kills the motion for the time being, and the motion can't be brought up again in the same meeting.
A motion may sound just fine on the surface, but in discussing it, you, and maybe others in your group, find the motion problematic and don't want to face having to vote on it. One example is being faced with a motion to express an opinion in the name of the organization about a controversial subject. A decision one way or the other could send the wrong message or even cause a split in the organization! The purpose of the subsidiary motion to postpone indefinitely is to defuse potentially damaging motions.
The motion to postpone indefinitely is a great tool for strategists. If you're opposed to the main motion, you can test the strength of your allies in opposition without risking the adoption of the main motion. Because debate on the motion to postpone indefinitely can go into the merits of the main motion, you can speak again even if you've exhausted your right to speak on the main motion. And if the motion to postpone indefinitely passes, you've effectively killed the motion for the present session. And if it fails, you're just back to the debate on the main motion.
The key characteristics of the motion to postpone indefinitely include:
Can't interrupt a speaker who has the floor
Must be seconded
Is debatable. (Debate isn't restricted to the pros and cons of postponing indefinitely, but may go into the merits of the main motion.)
Can't be amended
Requires a majority vote for adoption
Can be reconsidered if adopted
If a motion to postpone indefinitely is reconsidered and then fails, the main motion that it "killed" is alive again.