Selenium Locating Cell in Table Using Css

You're attempting to use the :contains pseudoselector in your CSS selector. This pseudoselector is not a part of any published CSS standard. Unfortunately, it's become common since the JavaScript CSS selector engine implementation used by jQuery (Sizzle) allows it to be used. Since the driver implementations rely on the browsers' native CSS selector engine implementations, they don't support the :contains pseudoselector, and throw the exception you're seeing. Also, I note that you're attempting to find the check box where the name attribute (not the element content) contains the string for which you're searching. In that case :contains wouldn't work anyway.

Leaving aside the inherent instability of finding elements using the text contained within them, if you really want to do that, finding by XPath is likely your only option. Also, the check box element is not a descendent of the element containing the text you're looking for. Rather, it's a sibling element, and CSS selectors don't permit you to walk up the DOM tree to parent elements. Again, this is a feature best handled by XPath.

I'd handle the issue using something like the following:

public void clickCheckboxInTable(String value, String action) {
  // Assume the WebDriver instance is stored in a class-level
  // variable named 'driver'.
  WebElement tableCell = driver.findElement(By.xpath("//td[contains(., '" + value + "')]"));
  WebElement checkbox = tableCell.findElement(By.xpath("..//input[contains(@name, '" + action + "')]"));
  checkbox.click();
}

Note carefully that this solution performs two finds. Doing so in two steps gives you the opportunity to perform other actions related to the cell containing your value if needed. Otherwise, you could use a single XPath expression like this:

// Using the 'direct parent' operator ('..'), but you could also
// use other axis functions like 'following-sibling'.
findElement(By.xpath("//td[contains(., '" + value + "')]/..//input[contains(@name, '" + action + "')]"));