First of all, let's create a new project using WPF template and place a button
in it as below:

Now, what I am going to do is, I am going to replace this content template for this
button. So, in order to do this, open up the Button tag and add Button.Template
markup tag with a new ControlTemplate as:

Now as soon as you will add ControlTemplate tag, you will notice that the
content of the button is gone and button is shown as a transparent rectangle.
This is happened because here I told WPF to replace the default ControlTemplate
with the one, which I defined. But at this point, our ControlTemplate is blank,
so there is no visualization and we can see only a transparent rectangle.
Now go ahead and customize our ControlTemplate by putting Ellipse inside it as:

Now we can see that, we get a visualization for a button in form of ellipse. At this
point of time, it works OK, but there are scenarios where this struct breaks
down.
For example, Let's increase the height of button, from 35 to 105 as:

In above image, you will notice that button height is increased but the ellipse size
is still the same, which is a bad UI design. And the reason this is happening
is, inside a ControlTemplate, the height of an ellipse is hard coding. So, no
matter, whatever height is set at parent (i.e. Button), it will not get inherited
to child control (i.e. Ellipse).
So, now we have to fix this problem by using a special type of binding called TemplateBinding
inside ControlTemplate. So, instead of hard coding the height, we will use TemplateBinding
as shown below:

By setting the TargetType property of ControlTemplate, we are telling Ellipse
that, any property of Button can be set to ellipse. Now, whatever the height
of button will be, it will automatically be the height of ellipse also. Isn't
it interesting?
Moving forward, let's do something more interesting with Fill property of ellipse

In above snippet, I am trying to set the Fill property of an ellipse using TemplateBinding.
But now problem here is, a button doesn't have a Fill property. So, there
is no one-to-one mapping for Fill property. Now, what to do ?
No need to worry that much because button does has a Background property as:

In above image, you might have notice that as soon as ellipse's Fill property
is set to Background, ellipse becomes transparent as button's background.
Now if we set button's Background property to Red, the same will be applied
to ellipse too.

So, one can understand that how much magic we can do with TemplateBinding.
Now, let's work little bit on code cleanup.
ControlTemplate inside resource dictionary:
For better code readability, we will move out our ControlTemplate code and put it
inside a resource dictionary as:

So, now we can see as earlier that whatever visual property for button is set, all
get applied to ellipse also.