Margin of error and confidence interval

I got this explanation of margin of error and confidence limit from a UK site:

"The margin of error of an opinion poll is often quoted as plus or minus 3%. This is a good approximation, but there is an exact formula that can also be used.

If an opinion poll sampled N people, and found a proportion p of support for a party, then the margin of error on that proportion is 1.96*Sqrt[p*(1-p)/N]. For instance if a poll of 5000 people estimates a party at 30% support, then the margin of error is 1.96*Sqrt[0.3*0.7/5000]=1.3%. Another example is a poll of 1000 people, and a party at 50% support, where the error is 3.1%, which is the famous "3%" margin.

This margin is not an absolute guarantee but a confidence limit. It should be expected that for 19 polls out of 20 the true levels will lie within the margin of error (95% confidence level)."