If you use "I was busy." the speaker is no longer busy at all, but if you use "I have been busy." the speaker is still busy or was until recently. Either way works though.

When you use the phrases "has been " or "have been" it shows a continuous action . So you are still doing that action . So " I have been busy this week " shows the speaker that you were busy the previous days and you still are busy even now . When you use the words "was" and "were " it shows past actions. Remember that these words are the past actions of "is " and "are" and in some cases "am" . "I was busy this week", shows that this week you were busy but not anymore .

When you use the phrases "has been " or "have been" it shows a continuous action . So you are still doing that action . So " I have been busy this week " shows the speaker that you were busy the previous days and you still are busy even now . When you use the words "was" and "were " it shows past action . Remember that these words are the past actions of "is " and "are" and in some cases "am" . "So I was busy this week", shows that this week you were busy but not anymore .