Any time you instantiate a class that Implements IDisposable, you should call .Dispose¹ on that class when you have finished using it. This allows the class to clean up any managed or unmanaged dependencies that it may be using. Not doing this could cause a memory leak.

The Using keyword ensures that .Dispose is called, without you having to explicitly call it.

For example without Using:

Dim sr As New StreamReader("C:\foo.txt")
Dim line = sr.ReadLine
sr.Dispose()    

Now with Using:

Using sr As New StreamReader("C:\foo.txt")
    Dim line = sr.ReadLine
End Using '.Dispose is called here for you

One major advantage Using has is when an exception is thrown, because it ensures .Dispose is called.

Consider the following. If an exception is thrown, you need to need to remember to call .Dispose but you might also have to check the state of the object to ensure you don't get a null reference error, etc.

   Dim sr As StreamReader = Nothing
    Try
        sr = New StreamReader("C:\foo.txt")
        Dim line = sr.ReadLine
    Catch ex As Exception
        'Handle the Exception
    Finally
        If sr IsNot Nothing Then sr.Dispose()
    End Try

A using block means you don't have to remember to do this and you can declare your object inside the try:

   Try
        Using sr As New StreamReader("C:\foo.txt")
            Dim line = sr.ReadLine
        End Using
    Catch ex As Exception
        'sr is disposed at this point
    End Try

¹ Do I always have to call Dispose() on my DbContext objects? Nope (opens new window)

Sometimes, you have to create two Disposable objects in a row. There is an easy way to avoid nesting Using blocks.

This code

Using File As New FileStream("MyFile", FileMode.Append)
    Using Writer As New BinaryWriter(File)
        'You code here
        Writer.Writer("Hello")
    End Using
End Using

can be shortened into this one. The main advantage is that you gain one indentation level:

Using File As New FileStream("MyFile", FileMode.Append), Writer As New BinaryWriter(File)
    'You code here
    Writer.Writer("Hello")
End Using