Sharing essentially means alerting someone to something in the community you want them to see. Maybe you know someone has a problem, and you found the answer, so you want to share it. Sharing only works if you care connected to the person. You cannot share with just anyone. This prevents a spammer from showing up and pointing you to nonsense.
Being connected means you follow them, or they follow you.
When you are looking at content (a document, discussion, etc), there is a Share button on the upper right portion of the page.
When you click, a dialog window appears. You type the name of the person you want to share with, or click the Select People button to see a list of the people you are connected to. You can share with more than one person at a time, as long as you are connected to them.