IQR, or Interquartile Range, is a robust measure of scale calculated by taking the third and the first quartiles in a set of data and subtracting them and is used in descriptive statistics. To find either of these quartiles, you must first find the median of a set of numbers. These two halves then have their own median which become the first and third quartile.
The IQR is a way to describe the spread of a set of data. This website describes when a data set has outliers, the interquartile range summarizes the variability. This is because the interquartile range is less sensitive to outliers explained here. Using the IQR you can build box plots for the graphical representation of probability distribution as this site puts it.
One use of the IQR is to detect outliers. After calculating the IQR, multiply it by 1.5. Now add this number to the third quartile, any number greater than this is a suspected outlier. Now subtract 1.5*IQR from the first quartile, and any number less than this is also a suspected outlier. These steps can be found here.
We use the interquartile range as an alternative to standard deviation because it is more susceptible to outliers and extreme values. Both are used summarize the extent of the spread of your data, but calculated in different ways for different reasons.