How To Change Contents Of Form Without Refreshing HTML Page

How do you update the contents of a form from a click of a button? I can poplate the contents of a table that is inside a form on the initial creation of the page

<form id="form1" name="form1" method="post" action="">
<p align="center">
List of Dying Patients
</p> <br><br>
<table border="1" align="center">
<tr>
<td>Last Name</td>
<td>First Name</td>
<td>Middle Initial</td>
<td>Date of Birth</td>
<td>SS Number</td>
<td>Marital Status</td>
<td>Gender</td>
</tr>
<script>
populatePatientsList();
</script>
</table>
</form>

and this is the contents of the function populatePatientList();
for (var x=0;x<mainArr.length;x++) {
document.write("<tr>" +
"<td>" + mainArr[x][0] + "</td>" +
"<td>" + mainArr[x][1] + "</td>" +
"<td>" + mainArr[x][2] + "</td>" +
"<td>" + mainArr[x][3] + "</td>" +
"<td>" + mainArr[x][4] + "</td>" +
"<td>" + mainArr[x][5] + "</td>" +
"<td>" + mainArr[x][6] + "</td>" +
"</tr>");
}

After this the table will have all the contents of the array. How do I reinvoke the form to have the updated version of the array shown on the table without refreshing the whole page? The page cannot be refreshed because the data is just in an array and when I do refresh the page the contents of the array gets back to its default. Is it even possible to refresh just a part of a page, in my case a table after a button click or are there other button events I can try to play with?