Research impact has traditionally been described in terms of academic prestige and publication metrics. However it is increasingly being thought of as the societal benefits accruing from research.The Australian Research Council now defines research impact as:
...the contribution that research makes to the economy, society, environment or culture, beyond the contribution to academic research.
The NMHRC recognises impact across four domains:
In terms of quantifying impact there is no single clear measure of impact. Various indices attempt to quantify scholarly impact using measures such as citations. Journals have impact factors, while altmetrics report on article usage. For ARC information on research impact see the file below.
Citation metrics measure the average citation count per article. They have their flaws, as many factors affect citation rates which have nothing to do with the quality of the research. The most well known is the H-index.
Metrics Toolkit: the h index.
Article: Explainer: what is an H-index and how is it calculated? The Conversation 2015.
Journal impact ratings measure the impact and prestige of journals. However publishing in journals with high impact factors may not guarantee the most relevant audience for a given piece of research.
Common journal ratings include:
Metrics Toolkit - Journal Impact Factor
Wikipedia - Journal rankings
Altmetrics measure output across a more diverse range of media including social media, online reference managers, page views et
Common altmetrics include Plum Analytics, Kudos and Altmetric.com.
Altmetric measures are commonly embedded in article pages.
Metrics Toolkit - Altmetric Attention Score 
Articles that are published under some form of Open Access tend to have greater impact.
This may be through be cited more (author impact), or by reaching an audience that does not have access to paywalled articles (societal, economic impact).
Article: The academic, economic and societal impacts of Open Access: an evidence-based review. F1000Research 2016, 5:632