Sounds like you would want to create two TVs. One Checkbox with a value of "Active" and one TextArea.
As far as I know, having it display the textarea when box is checked cant be done. At least I have never seen it. Maybe somebody more advanced knows how, if this is possible.
Assign both new TVs to the template.
In the template, you would include an
If statement, something like:
[[if? &is=`[*MyCheckbox*]:contains:Active` &then=`<span>[*MyTextArea*]</span>`]]
Maybe this is of some help, I hope. Or more in the direction of what you want to do?