Margin of error
Also called sampling error, MoE
An estimate of sampling uncertainty around a survey percentage, stated at a chosen confidence level.
A margin of error is reported in percentage points and attached to a confidence level: ±4 points at 95% confidence means that if you drew many random samples the same way, about 95 of every 100 would land within four points of the population figure. It describes the wobble that comes from asking some people rather than everybody.
It is widest when a result is near 50% and narrows towards the extremes, which is why a survey-wide margin is usually quoted at 50%: it is the worst case, so nothing in the survey is less precise than the headline. Subgroups get their own margin, computed from their own n, and it is always wider than the survey's.
What it does not cover is everything that is not sampling: who declined to answer, whether your list reached the right people, whether the question was understood. A large opt-in sample can carry a margin of ±1 point and still be wrong by twenty.
Worked example
400 responses at 95% confidence gives ±4.9 points. A finding of 62% is consistent with anything from about 57% to 67%.
Where it goes wrong
Comparing two numbers by checking whether their intervals overlap. Overlapping intervals are not a test, and non-overlapping ones are a conservative one; run the test instead.