Metrics that aim to demonstrate the impact of an author over their total research history or within certain time periods can be useful for academic promotion submissions, applying for new roles in academia, and for funding applications.
The h-index is a measure of both productivity and impact of ones published works. It looks at the total number of papers you have published, and the number of citations those papers have received. It is based on the highest number of papers included that have had at least the same number of citations.
For example, if you've published 2 papers, and each paper has been cited 2 times, you will have a h-index of 2.
What if it's a little more complicated, where your published papers have range of both high and low citations? Let's say you've published 5 papers altogether, one cited 5 times, one 4 times, one 3 times, one 2 times, and one just the 1 time. You will have a h-index of 3. That is to say, you cannot claim higher (4 papers cited 4 times each).
Thus the h-index attempts to measure the impact of your output - you need to have published a large number of papers, which were in turn cited a large number of times, to have a high h-index.
Limitations of h-index
The h-index is not appropriate for comparing across disciplines and disadvantages early career researchers.