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PDF is a file format by Adobe which stands for "Portable Document Format". See info on Wikipedia.
Printing to PDF is very useful. If you purchase something online and they have a "print receipt" link and you don't have a printer hooked up, you can print to a PDF document and store it on your hard drive (and for later printing if desired). If you want to send someone a document that you don't want them to alter, you can write the document in your favorite text editor (Microsoft Word for example) and do a "print to PDF" and email the PDF document to the person. Obviously you don't want to email the Word document, as it can be easily altered.
PDFs are very prevalent. Nearly all computer users (PC and Macs) alike can view PDF files. Google can even index and search through them. There are many free PDF readers out there. But why not get it from the makers of PDF themselves -- Abobe Reader is free on the Abobe website.
Although the Abode Reader lets you view and print PDF documents that someone has given you, it does not let you generate PDF documents.
I use Adobe Acrobat which comes with a printer driver which installs into my Windows operating system. So now every Window's print dialog has the option of printing to my printer or printing to a PDF file. With this, if I want to print to PDF from Microsoft Word, from my browser, or from any application that has the Windows print dialog, I just do the normal "File -> Print" and select "Adobe PDF" from the list of printer and it will ask me for the filename to save the PDF to. Adobe Acrobat also give you the ability to combine multiple PDFs into a single PDF document.
There are many other ways of doing the same and to generate PDF (some of which are free). The following are some that you might want to consider ...