Impact Factors - From ISI (Institute for Scientific Information a part of Clarivate), are a method for attempting to assess a journal's influence and are more widely used in the sciences and social sciences.  They are based on the number of citations articles received in a given journal divided by the total number of articles published in that journal all over a given time period.  You can locate impact factors from the Journal Citation Reports which has a link on the Web of Science database home page.  

Article Level Metrics - SPARC (Scholarly Publishing and Academic Resources Coalition) - offers an overview and analysis on article level metrics.

Altmetrics - or "alternative metrics" is a new area that uses article level measurement such as downloads, pageviews from publishers, collaborative annotation tools, amount of online discussions and more to assess importance.  Resources:

Metrics Toolkit - a toolkit that provides guidance for demonstrating and evaluating claims of research impact.  Created by IUPUI.  

Altmetrics.com - a company that provides altmetrics data for researchers.  They provide a free bookmarklet for researchers, as most of their products cost money.  

Impactstory - an open source tools that allows researchers to monitor altmetrics for their publications.  A Twitter account or ORCID ID are required to particpate.