If the user presses the first button, then the value in that textbox with the button will be available at the server side.
For example, if the user enter the value "a", "b", "c" in each of the textboxes and presses the first form's button, then the values available in the $_POST array would be:
If it was the second button that the user pressed, then the values would be:
Array ( [Name] => a [button1] => reserve )
And for the third:
Array ( [Name] => b [button2] => reserve )
That is, when you access the "Name" element of the $_POST array like this:
Array ( [Name] => c [button3] => reserve )
you will get the value from the textbox belonging to the form, which the user had pressed the button.
Hope it's clear. Let me know if you are still having trouble understanding it.