Since not enough of the reading audience have been magically transformed into math geniuses by a very specific genie yet, we'll let Statistics For Dummies spell it all out slowly for us: "P is the sample proportion, n is the sample size, and z is the appropriate value from the standard normal distribution for your desired confidence level." Yikes. Just know that there's a formula out there that explains how dumb we all are when it comes to polling.
Conventional wisdom says that the smaller the margin of error, the better. And it also stands to reason that the more people you survey, the smaller it gets, right? Here's the thing, though: Modern experts "disagree fiercely" about when and if the whole margin of error thing should even be used at all. Not to mention -- and hold onto your hats, because this may be a nearly inconceivable revelation coming up here -- it turns out the people doing the polling can't always be trusted.
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Editing your gun control "yea" to a Flat Earth trutherism one is one stroke of whiteout away.
Besides the fact that talking to a few hundred (or even thousand) knuckleheads can never be a precisely accurate representation of the beliefs of a nation of hundreds of millions, something called "biased sampling" on the part of the pollsters can further skew the results away from reality. Let's say you want to know who "the people" consider the greatest singer of all time. And because you're lazy and live next door to a nursing home, the only people you poll are on the closer-to-death side of 75 years old. That's biased sampling. Also, good luck quelling the riots between the Johnny Mathis Mafia and the Tony Bennett Gang.