Robust confidence intervals are like a type of insurance - they help you to make sure that you won't be misled by results that don't reflect the reality of the data.
Imagine that you have a jar of coloured balls and want to find out how many of each colour there are. You could just count how many of each colour you have and calculate the exact numbers of each. But what if one of the colours looks more red than it is, so you count it twice? Then your totals would be inaccurate.
Robust confidence intervals help you to check that this kind of mistake won't happen, by giving you a range of possible values: a lower limit and an upper limit. This range shows you the minimum and maximum number of items that you could have in your jar, plus a certain amount in between. So even if you make a mistake, like counting a colour too many times, you won't be too far off when you estimate the overall numbers.