I am the original developer of iText and the CEO of the iText Group. I'm also a Mentor at the Founder Institute. Please take a look at my slides for the session about Startup Legal and IP for the Founder Institute. I've also won a JavaOne Rock Star Award granted to me by the audience of my talk IANAL: What Developers should know about IP and Legal.
iText is software and therefore copyright law applies:
Copyright law allows an author to prohibit others from reproducing, adapting, or distributing copies of the author's work.
According to the copyright law, you do not have the right to use software that you didn't write yourself.
However, iText is distributed using a copyleft license:
Copyleft gives every person who receives a copy of a work permission to reproduce, adapt or distribute the work as long as any resulting copies or adaptations are also bound by the same copyleft licensing scheme.
This means that anyone can use iText for free as long as the conditions for its use are met.
To know more about the conditions, you need to take a look at the license. In this case: the AGPL. This means that:
You can not distribute a closed source application that is based on iText without distributing the full source code of your own application.
You can not use iText in a web application without making the full source code of your web application available through that web application.
This is why people often refer to the AGPL as a viral license: all the software that touches an AGPL library such as iText needs to be free too.
Obviously, there are plenty of companies who do not want to ship their source code. That's why iText Software also provides iText under another license. This license is a commercial license. You have to pay for it.
To answer your question: iText can be used for free in situations where you also distribute your software for free. As soon as you want to use iText in a closed source, proprietary environment, you have to pay for your use of iText.