Facebook gives the facility to chat online with your friends but sometimes you may not want them to know your online, so you have the facitiy to show your status as offline.
To go offline
Select the cog
Select Go offline
The background profile picture and names of your contacts will pale over and the green dot showing who is available to chat will disappear
To go online
Select the blue Go online
Your contacts profile images will appear clearer along with their names, and any that are availalbe to chat will have a green dot next to their name. If they have a little mobile phone instead of a green dot it means that any chat message you send to them will be sent directly to their phone.