Following are some use cases and examples for this:
a) Common use of this is to specify the connection string property of a control.
<asp:SqlDataSource ID="SqlDataSource1" Runat="server"
SelectCommand="SELECT * FROM [Employees]"
ConnectionString="<%$ ConnectionStrings:TraineeDatabaseConnectionString%>">
</asp:SqlDataSource>
Inside Web.config:
<!--A common use of expressions is to set the connection string property of a control-->
<connectionStrings>
<add name="TraineeDatabaseConnectionString"
connectionString="uid=trainee;pwd=mindfire;database=Trainee2009;server=LANSERVER;"
providerName="System.Data.SqlClient" />
</connectionStrings>
b) To display static content in our web pages we can add key-value pair in <appSettings> .
For example, Lets set a key value pair inside Web.config for the copyright message for our website.
<!--setting the site's copyright message-->
<appSettings>
<add key="copyright" value="(c)Copyright 2009 MFS"/>
</appSettings>