I answered in a different way, but it works! Can I improve it?

If you wanted to combine your solution with Dave's print() function, this would be one way to do it:

var message = "";
var student;

function print(message) {
  var outputDiv = document.getElementById('output');
  outputDiv.innerHTML = message;
}

for( var i = 0; i < students.length; i += 1) { 
    student = students[i]; 
    for(var prop in student) { 
        if (prop === 'name') { 
            message += '<h2>' + prop + ': ' + student[prop] + '</h2>';  
        } else {
            message += '<p>' + prop + ': ' + student[prop] + '</p>'; 
        }   
    }
}
print(message);

In a sense your solution "feels" more elegant by utilizing and printing the property names, but in practice it may have some problems. The more minor problem is that it makes formatting the output difficult, in particular if the property names in the object/array are not labeled exactly how you would want to output them. The more significant problem would be if there were additional properties in the student array that you did not want to output at all. You could filter them out, but the loop would still have to go through each of them and in a very large array with a lot of values, this would be an expensive operation.

But it's still good that you came up with a different solution. There are often different ways to accomplish the same thing, and your way may well be better in some instances.