Sharing is allowing specific users to have access to content you own, or content that has been shared with you.
To Share Content
Click on the Sharing tab to access the sharing page for any piece of owned or shared content. Scroll down to the Add sharing permissions to users section. Tip: For folders, be sure that you're sharing the actual folder, and not a display page for a folder. If you see a message highlighted with an orange box then you are sharing a page, not a folder. To share an entire folder, be sure to click on the Contents tab, and then the Sharing tab.
Search for the individual by Full Name. Their name should appear in the results. Tip: It is sometimes best to search by using a person's last name only. The name has to match the directory exactly (e.g. John T. Doe vs John Thomas Doe) so it is sometimes easier to pick a name from a list of results with the same last name.
Check the box next their name under Available Users, select the role to assign, and click assign local role to selected user(s). The added user should now appear under Current sharing permissions… and have the specified ability to operate within that part of the site immediately.