You can use the phrase when you can't remember something that should already be in your brain no matter how hard you try to remember.
“ド忘れ” is kinda funny word, and it means a frustrating situation that “you know the name or something of that stuff, but you just can't remember it for some reason right now.”
It expresses your feeling that “I do know the stuff, and I just can't remember it right now.”
Is there a good way of putting it in English?
You can use this phrase when you'd like to say “I completely forgot (to do) something.” or “It slipped my mind.”. It's used when you forgot an appointment, a deadline, homework and etc.
You can also say 「すっかり忘れてた。」.
Example: 「この前貸したＣＤ持って来てくれた？」 ⇒「ごめん、すっかり忘れてた。」
“Did you bring my CD? ”⇒ “I'm sorry. It completely slipped my mind.”
Oppositely, if you have it on you, you can say 「大丈夫、持って来たよ。」
It's the same as to be forgetful. “I'm forgetful.” is 「俺(ore)は忘れっぽい。」or「私って忘れっぽいんだよね。」
You can also say to describe that you're forgetful. : 「物忘れ(monowasure)が激(hage)しい。」、「すぐ忘れちゃう。」、「なかなか覚(obo)えられない。」
I found out that it sometimes is more difficult that you explain phrases or words in your native tongue than try to learn another language.
I hope it could, and let me know if you have any unclear part.