That's a very broad question and I see that it already has a vote to close the question for this reason. Let me give the nutshell version of the answer. I could easily write a book on this topic (and maybe one day I will).
iText is a library that can be used by developers to enhance their web and other applications with PDF functionality: create PDF, fill out PDF forms, examine and manipulate existing PDFs.
JasperReports is a Business Intelligence / Reporting tool that uses an old iText version to create reports. It is distributed by JasperSoft / TIBCO. JasperReports only uses a limited part of the complete iText functionality. Creating PDF is just one of many features of JasperReports, and JasperSoft uses iText to implement that feature.
Adobe LC is a suite of modules, some of which can only be provided by Adobe. For instance: no third party can "Reader enable" PDF documents because Reader enabling requires a private key that is proprietary to Adobe. However: iText competes with Adobe LC in some areas, for instance digital signing (read the white paper from the Office of Legislative Counsel on digital signatures) and form filling (iText has an add-on called XFA Worker that can convert your dynamic XFA forms into static PDF, e.g. PDF/A)
Click this link if you want to see how to answer this question in iText 5.