The phrase "first author" refers to the person who has contributed the most in writing a research paper or a scientific article. They are typically the primary writer and have played a significant role in conducting the study. Full definition
Objective To examine changes in representation of women among first authors of original research published in high impact general medical journals from 1994 to 2014 and investigate differences between journals. (bmj.com)
They are the ones who are cited as first authors on the papers in the field; that is an amazing legacy for us. (asbmb.org)
Different members of the lab should also be listed as first authors, because this will show that projects and credit are distributed. (sciencemag.org)