GZip is the GNU Zip compression system. Its chief advantage is (or was, at the time) that it is unencumbered by certain software patents.
It is common for web pages to be transmitted in a compressed form to reduce transmission time and bandwidth, and GZip is a common choice automatically handled by all browsers. Downloadable files and folders (directories) may also be compressed (with GZip or other methods) to reduce their size, but will typically need the user to take some explicit action to uncompress them on the receiving end and make them usable. Note that "tarring" or "archiving" a set of files (such as a folder) is technically a separate thing from compressing the file(s), but they are often combined into one operation.