Adobe Reader is one of the most popular programs on the Web. It's a free program that lets you easily view and sign PDF documents that anyone sends you. Since PDF documents are incredibly important, Reader is on most computers.
Adobe Acrobat is a little more popular in design circles. It's a paid program that edits and creates PDF documents from scratch. Businesses and graphic designers use it extensively.
Hackers frequently target both programs and so you need to install the frequent updates to keep hackers at bay. That's why I've rounded up links so you can make sure you have the most recent versions.
In order to download and use the updated versions, you must have a version of the program already installed. Adobe might also try to install Google Chrome and an Adobe toolbar as you're trying to update. Make sure you opt out of these if you don't want them.
If you'd like to skip the whole process entirely, you can dump Reader for another PDF program. Sumatra, Nitro PDF and Foxit Reader are all good choices. Some browsers have a PDF viewer built in, too.