What does a checkbox that is filled mean in Windows?

It means some options of the subtree of options of that option are selected or that the box is checked for some of the objects.

E.g. when using a single properties dialog for multiple files. If you select files one, two and three, and only two and three are "read-only", the checkbox will look like that. However, if you select only two and three, the checkbox will look checked. If you select only one, the checkbox will be unchecked.

Sometimes an option tree is used like the one below.

[] My meal
    [] Sandwich
        [] Bread
        [] Cheese
        [] Butter
    [] Drink

So if all options below "My meal" are checked, so will "My meal". But if only one is not (doesn't matter if it's "Sandwich" as a whole or just a sub option of "Sandwich"), "My meal" will be like on your screen shot.

Programmatically speaking, There are 3 states to a Check Box - Checked, Unchecked and Indeterminate.

• Checked - All items satisfy the criteria.
• Unchecked - No item satisfies the criteria.
• Indeterminate - Some of the items satisfy the criteria, or it's unknown whether the box should be checked or not.

Example - http://msdn.microsoft.com/en-us/library/ms743611(v=vs.85).aspx

The following graphics illustrate the three states of a CheckBox. The graphics show a dialog that shows the properties of files in an application called accesstext. The attributes of the files are indicated with a CheckBox. In the first graphic the file is Read-only (CheckBox is checked) and the second is Read\Write (CheckBox is unchecked). In the first two graphics the information concerns only one file Pane1 but the third graphic concerns all the files in the accesstext application. Some of the files are Read-only and some are Read\Write the attributes for the entire application cannot be determined (CheckBox is null).

Checked

Unchecked

Indeterminate

The checkbox has three states:

• white, empty: This option is NOT selected (and none of it's sub-options, if any)
• green: Some sub-options are selected, some are NOT
• ticked: This option is selected, if it has sub-options, all of them are selected.

What does it mean for a directory? And I've tried to uncheck the reason-only attribute and apply it recursively several times,but it still shows like the 1st checkbox...

Your comments indicate that you're looking at folders in Explorer, so here is the obligatory Old New Thing link to answer the question you really have: Why is the readonly property for folders so strange?

What it boils down to is that the read-only and system flags tell Explorer to check the folder for a desktop.ini file that specifies folder customisations. Most programs ignore the read-only flag for folders, at least in the traditional sense of "don't allow anything to write to this folder." That's why you see the indeterminate status in Explorer.

There's also MS KB Article 326549:

The Read-only check box for folders is not available because it does not apply to the folder. You can use this check box to set the Read-only attribute for files in the folder. However, you cannot use Windows Explorer to determine whether a folder has the Read-only and System attributes set. To determine the attributes that are set on a folder, or to change these attributes, you must use the Attrib command at a command prompt.