The "room for error" since the poll is based on a sample and not the whole population. It tells us how much the result might be "off" by determining if the data is significant, or just statistical noise.
A smaller margin of error means the poll is more precise, and the larger the sample size, the smaller the margin of error usually is.
If a poll says: "52% support Candidate A, with a margin of error of ±3%". That means the real number of people who support Candidate A could be as low as 49% or as high as 55%.
You should consider MOE when:
The Margin of Error is LARGER than the difference in support between candidates or issues; it means that "real" support could overlap, and the comparison is statistically tied.
If a poll says: "Candidate A leads Candidate B 48% to 46% with a ±4% margin of error".
In these cases, we should be cautious when relaying this information because support could overlap due to the MOE being larger than the difference between support for candidates.