The SERP is the page that search engines show in response to a query by a searcher.
This page will look different depending on the search engine (Google, Bing, Baidu) but the main component is the list of websites or blue links that provide answers to the query.
Source: HSMAI CHDM Study Guide
The definition of a “Brand SERP” is “The set of results that appear when someone searches for a brand on a search engine online”.
Or, to put it another way, it’s what you see when you use a brand name as a keyword.