expression
this is why; that means; so it is that
A phrase used to sum up a reason or conclusion, often after an explanation. Equivalent to 'that's why' or 'so that's the situation'.
彼は昨日遅くまで働いていた。というわけで、今朝は寝坊した。
He worked late last night. That's why he overslept this morning.
つまり、計画は中止になったというわけだ。
In short, it means the plan has been canceled.
つまり is a conjunction meaning 'in short' or 'that is to say', used to rephrase or summarize. というわけだ is a phrase that concludes with the reason or result, often at the end of a sentence.
だから is a simple 'so' or 'therefore' linking cause and effect. というわけだ adds a nuance of 'this is the reason/explanation', often after laying out facts.
From と (quotative particle) + いう (to say) + わけ (reason, conclusion) + だ (copula). Literally 'it is the reason that one says', grammaticalized into a fixed expression.