Publishing is when you save a copy of your place to the Roblox servers. This means that it saves your place, and then uploads it to the Roblox servers, where it is stored so others can enjoy your place more easily.
Please note that you can save your game to Roblox (and/or as a local copy) without publishing your game. Saving to Roblox will save your progress without it being publicly accessible, while publishing to Roblox will save your progress and make it available to play.
For more information about how to publish your place to Roblox, please refer to the "Saving and Publishing" section of our Roblox Studio Overview.