What is a Web Browser Extension?
A web browser extension (or plugin, or addon) is a software that you install on your web browser that adds functionality to the web browser.
Web browser extensions are relatively safer than normal applications because a normal application can delete all your files, while a browser extension can only steal all your passwords that you use on your web browser.
More specifically, because the extension is running on top of the web browser, the web browser can restrict the operations the extension is able to perform. It generally won't allow an extension to access your files, for example. However, many extensions that modify content of websites and webpages require FULL ACCESS to those webpages' content in order to modify it. This means anything that is written on the webpage, such as your username, or information like how often you access that website, is accessible to the extension. This doesn't mean the extension is going to use this information for malicious purposes, but it COULD use it for malicious purposes if it wanted because the information is available to the extension.
In particular, many developers of free browser extensions are frequently contacted by companies that want to "help" monetize those extensions by harvesting the users data. The company would pay the developer, who would modify the extension to harvest the user's data and send it to the company without the user having any knowledge that such thing is happening.
Some browser extension stores, like Google Chrome's, may vet extensions that are uploaded to the store checking for abuses like this. I'm not sure if it really works, but, from what I read, the more permissions an extension requires, the more thoroughly it will be checked by the store. Considering how many extensions are available today, this "checking" is most likely fully automated, so there could be ways to bypass it by evil actors that really want to exploit the system. While it's a great service to offer, it's not perfectly safe, so always use precaution when installing browser extensions, specially from developers whom you don't have any reason to trust.