The h-index aims to measure both the impact and productivity of a researcher. H-index is calculated by comparing the total number of a researcher's papers with the total number of citations each paper has received. A researcher who has published 5 papers, each of which has been cited no less than 5 times, will have an h-index of 5.
So, h-index allows us to evaluate the impact of a researcher rather than relying on the impact factor of a journal in which that researcher is published. Moreover, it allows us to take a more holistic view of a researcher's productivity by eliminating a potential skew towards a single influential paper.
However, the h-index still cannot capture the nature of a citation or informal citations (blog posts, tweets, etc). Moreover, the h-index favors later-career researchers, as the potential h-index score will always be limited by the total number of publications a researcher has produced.
Citation count--the number of times other researchers have cited your work--may be the most heavily-used article-level metric.
You can also find out how many times an article has been cited through Google Scholar.
While an important indicator of the impact of a researcher's work, citation counts only capture a singular kind of use--citations. Impact may be more broadly tracked with the addition of Altmetrics.
Citation counts are an important metric in determining the impact of your work. However, the research and publication process can be slow--it may take years for an influential article to receive its first citation. In addition, citation counts are narrow in that they do not capture the context of a citation or the use of the work in informal communication pathways (Facebook, blogs, etc), or outside of academe, such as news reporting.
Alternative metrics (Altmetrics) can be faster and broader. Tweets, downloads, Facebook mentions, and Mendeley shares happen rapidly on publication and can provide some context on how your work is being used. In addition, you can use altmetrics to track the impact of less formal forms of scholarship like datasets, blog posts, presentations, etc. While unlikely to replace citation counts, altmetrics can help you illustrate your impact in rapid and contextualized ways.