When you publish a map service you define the ArcGIS Server path you are wanting to publish to like http://Myserver:6080/arcgis. Just like the example url that is provided in the dialog that appears when you add a server to publish to.
You may want to look at the tutorial Tutorial: Publishing a map service—Documentation (10.3 and 10.3.1) | ArcGIS for Server and the help page Approaches for publishing services with ArcGIS—Documentation (10.3 and 10.3.1) | ArcGIS for Server To get a better understanding about the process.
This is assuming that you are asking about ArcGIS Server. If this is the case, you may also want to look at Moving Content and move this to the ArcGIS for Server space ( other spaces can be fount GeoNet Community Structure )
since it sounds like you are still having questions after looking at the tutorial, first question, do you have ArcGIS Server installed? If you don't, then the http://my server:6080/ArcGIS wouldnt work. If you do, the "myserver" portion of the oath would be the name of the server box that the ArcGIS server software is installed.
if you do not have ArcGIS Server, you may want to think about publishing to an ArcGIS Online account.
it would help if you could include a few more details about what you currently have, and what you are trying to do. Otherwise we are just guessing or how we can help.
Yes im tring to publish ArcGIS Server. Yes, you r right I didnt install ArcGIS Server. Plz help me how to download ArcGIS Server..?
Otherwise I have ArcGIS account , can i publish in "My Contents" place...?
Thank You for your Information.
ArcGis Server is a licensed product, and is only downloadable if you are licensed. It sounds like you do not have a license, since it's not a cheap product...so you would know if you had it.
for publishing to ArcGIS Online, I would check out Publish hosted feature layers—ArcGIS Online Help | ArcGIS If you only have a free ArcgIS Online account, there may be limits to what you will be able to do. You may also want to look thru Frequently asked questions—ArcGIS Online Help | ArcGIS Which may answer some of your questions.