How to verify if HTML table sort is stable or not?
From a once over;


The easiest way to be sure that you sort algorithm is stable, is to write you own sort algorithm.
The second easiest way to be sure is to pass in each array entry object it's position in the array ( you could set this after your arr[i][j] assignment ). If (a[c]==b[c]) then you would not return 0, but you would return -1 or +1 based on their original position in the array
You did not declare c and asc with var
var arr = []; is preferred to var arr = new Array();
One single comma separated var statement is preferred over many var statements
You declare var i twice, since var i declares i for the scope of the function, you do not need to declare it again.
Your indenting is off, you should look into that
Assigning a function to document.ready is old skool, you should look into using addEventListener or simple using $( handler );.
You should cache the value of a&lt;$("tbody tr:eq(0) td").length

 for (var a = 0, count = $("tbody tr:eq(0) td").length; a &lt; count ; a++)

On my second point, imagine you are sorting people by their age, in a stable manner:


Bob, 23 years
John, 12 years
Tricia, 23 years

becomes

Bob, 23 years
Tricia, 23 years
John, 12 years

it would be unstable if the order was

Tricia, 23 years
Bob, 23 years
John, 12 years

because Tricia was initially below Bob, she should stay below Bob. 
You can accomplish this by comparing the original position of the 2 records and making sure that if the age is the same, you make sure the original order is respected.

I hope this example made it clearer.