gmail
I'm having a strange issue in Gmail.
I couldn't edit the text that was already typed. It overlaps the existing text. The cursor itself looks boxy instead of line.
It's hard to explain with text, So here is a GIF what I mean.
Any idea how to get rid of this annoying thing?
Some details
I tried refreshing my Pinned Tab, But it still exist. When I opened in a new tab, it works fine but again after some days, again the same issue.
Can you try by changing your text area from plain text to rich text or viceversa, also can you check you gmail account under another webbrowser. If still you are finding the issue you can contact GMAIL directly 
Just to provide some background: Right now, it doesn't seem like you can turn this feature off.
There used to be a labs feature to turn "quote selected text" on. Very recently (mid-November '12) they turned it on by default, without providing a way to disable. I haven't been able to find any official mention of it, only comments from others who have noticed the change and miss the old way.
Best Answer
As mentioned in comments, what you are experiencing is consistent with being in "overtype/overwrite" mode, as opposed to "insert" mode (the usual default). This mode is usually toggled by simply hitting the Insert or Ins on your keyboard. (Which might require a key combination on some keyboards - particularly laptops.)
I get the same result if I hit the Ins key whilst composing a Gmail message, although there is no indication as to the selected mode in Gmail (or the browser) itself.
Bizarrely a lot of other people seem to have experienced the same problem in Gmail without having knowingly triggered overtype mode on their keyboard. Although the threads I've seen on the subject don't appear to be entirely conclusive, it maybe that on some keyboards, overtype mode might be triggered inadvertently with some alternative key combinations.