There is multiple problem on your code.
First, you made a mistake on your date comparaison
if (dateColumn[i] = todaysDate) {
instead of
if (dateColumn[i] == todaysDate) {
Also, the best way to compare date is to compare the time by using getTime() method. See also this SO question : Compare two dates with JavaScript
You try to use the Sheet.setTabColor(String) method which modify the tab color of the sheet, when you try to get the Range.setBackground(String) method or the Range.setBackgroundRGB(red, green, blue) method.
Here is a solution:
function colorEntireRowGreenWhenDateOfEventMatchesCurrentDate() {
var data = SpreadsheetApp.getActiveSheet();
var range = data.getRange("C2:C15");
var values = range.getValues();
var today = new Date();
var todaysDate = new Date(today.getFullYear(), today.getMonth(), today.getDate());
Logger.log(data);
range.setBackground(null);
for (var i in values) {
var d = values[i][0];
if (d.getTime() === todaysDate.getTime()) {
var row = parseInt(i) + 1;
data.getRange(range.getCell(row, 1).getRow(),1,1,data.getMaxColumns()).setBackground('#3c643c');
}
}
}