Server Object Model
1-SharePoint itself uses the server object model.You can also use this model on a sharepoint server bcz it has some dependencies satisfied by the sharepoint server.
2-Here you can use LINQ programming like LINQ to SharePoint.
3-different classes are there like SPFarm, SPServer, SPService, and SPWebApplication etc.
Client Object Model
1-Use in case you want to develop client solution that interacts with SharePoint 2010.
2-It is available in three different flavors like: .NET managed,Silverlight and ECMAScript.