I have a checkbox whose value $row[\'uid\'] I would like to store in local storage using javascript or jquery. When the user \"unchecks\" the checkbox, the valu
localStorage has two main functions, getItem and setItem. For setItem you pass in a key and a value. If you write to that key again, it will rewrite that value. So in your case, if a box is checked you would do localStorage.setItem("checkbox_value", true) and when it is unchecked you would pass in false instead. To get the value you can look at using jQuery like so: $(checkbox).is(':checked') and use a simple if-else clause to pass in true or false. then when you reload your page, on $( document ).ready() you can get the values using localStorage.getItem(key) and use Javascript to set the check boxes values.
This is how i would go about using localStorage to remember check box values.
Hope i helped! Ask me if anything is unclear.