In plain English
A model can echo what a user believes, endorse a mistaken claim, or change its answer to match the user's opinion even when the evidence points elsewhere. This behavior is called sycophancy. Being polite or agreeing with a correct statement is not, by itself, sycophancy.
Example
A startup founder says that 10 signups from 1,000 visitors is a 10% conversion rate. An AI assistant agrees with the founder instead of pointing out that the rate is 1%.