There are really two numbers that have to be considered, although the news always drops the second one, which is the confidence interval.

So take the example in the OP. Smith has 49% and Jones has 46%. The margin of error is 3%.

That Wiki article assumes a confidence interval of 95%. We don’t know this, because that depends on the size of the sample. However as a first step let’s accept it.

Therefore there is a 95% chance that the actual percentage in the population for Smith is somewhere from 46% to 52%. (Or, another way, there is a 1 in 20 chance that the number lies outside this range.) There is similarly a 95% chance that Jones has 43% to 49% of the population.

Jones could be leading Smith. Jones could be far behind Smith. And one in 20 times both numbers could be wildly wrong.

The confidence interval is tied to sample size, so knowing the size of the sample is important. A larger sample - assuming that it is a good random sampling - will likely be wrong in fewer cases. And you can break down a larger sample in groups - male, female; black, white; young, old - with more confidence. That’s why the “real” Nielsen ratings don’t go by the 1000 or so homes that have meters but by the 10,000 that keep diaries. You can’t break down a sample of 1000 into dozens of smaller groups with any confidence.

Of course, in the real world there is no such thing as a truly random sample. All real world surveys are adjusted to make up for the groups that are underrepresented. Each survey outfit has its own proprietary algorithms for weighting samples, some of which are better than others, which is why they give better results. None work all the time.

Does all this make polls ridiculously unreliable? No, just plain ordinary unreliable. The real problem with political polls is that many, many people don’t make up their minds until they get into the voting booth, and not all of them admit to being undecided to a pollster. And even a 1% margin of error is useless if the final vote margin is less than one percent.

The secret to political polls is to watch trends among many separate polling companies. And even those are still vulnerable to massive mind-changing, as often happens in primary season.

Which is more than the question asked, but it’s hard to stop when this comes up.