Open source can be a project where the goal is to have a free software than replaces a paid software or does something that has never been done before. Open software does not have to be free software. It can just be a development model. Whether the goals are for profit, replacement of software, or a new function, the open source model offers the most advantages to development.
Look at how software is traditionally developed. A company or group of people will find paid programmers to make the software. They will oversee the programmers directing them as to what they want. Eventually the software is created. Generally this software is either sold or used for internal use.
The open model offers a wide range of advantages.
First, instead of having a limited number of programmers there can be thousands of programmers. When there is a thousands of lines of code, a limited number of people might not find the bugs or problems. When there are thousands of eyeballs on that code from a variety of backgrounds, it's more likely that mistakes will be found. When these mistakes are fixed, typically there is better performance and more security for you when using these applications.
Another advantage is that with more people, there will be more perspectives. If the group can make changes, they can come up with better ideas than intended. Pain programmers are paid to do what they are told. Open source programmers do what they feel is best and this can end up being more innovative. There are a wide variety of very popular scripts and applications that are open source that have brought the most innovative ideas.
In open source the programmers are volunteers. There are thousands of programmers who do it because they are passionate about the project. Passion typically gets better results than doing something because you have to do it for a paycheck.
The two models of software development are paying programmers to write software and the open source model. Open source projects offer distinct advantages that paid programmers can't compete with.