Extensions (or add-ons) are software components that, once integrated with your browser, allow you to expand its functionality, adding new features to the browser or modifying existing ones. They are useful in practice to improve the browsing experience, giving you the possibility to perform activities not otherwise possible by default with the browser.
They are free and almost always developed by third parties (i.e. not by the browser), so they are called a third-party extension.
Who are those third parties? There are a number of programmers and developers who create such extensions for the purpose to advance the browser they are personally using, or for the purpose to offer the world an idea, a concept made into a useful little program.
The modern concept of software development
This often implies the inclusion of only basic functions in the main program, and additional functionality is realized with the help of add-ons. Browsers are typical representatives of such an ideology. Of course, you need to understand that the basic functionality of any program is not a constant thing.
Programs are constantly evolving, acquiring new opportunities and discarding unnecessary ones. What initially appeared as an addition with time can enter into the basic functionality of the program. Often the developers of add-ons are completely outsiders or organizations that are not related to the developers of the main program.
People who need to be aware of the weather forecast or know the exchange rates can install such extensions. Of course, you can go to the relevant sites on the Internet and look there, or you can just install the appropriate extension in the browser and always have the necessary information before your eyes on its panel.
The plug-in can add support for any data format to the browser, and they can be viewed directly in the browser, without downloading to a computer and opening it in a third-party program. These examples are just tiny examples of what can be done with extensions. The possibilities are limited mostly by the imagination of developers and demand.