つまり
That is, in other words, in shortmachine translation
FormationAt the start of a sentence or mid-sentence: A。つまり、B。/A、つまりB
つまり is used when you RESTATE what you just said in a clearer way, or draw a conclusion: 彼は母の弟です。つまり、私のおじです (he is my mother's younger brother. In other words, my uncle). What follows つまり must have the same content as what precedes it, only phrased differently.
Two familiar uses: explaining a roundabout relationship or concept with one neat word (…つまり伯母です); and summing up what the other person said in order to confirm it: つまり、行きたくないということですね (so in short, you don't want to go, right?). The second type very often ends with ということだ.
Distinguish: したがって draws a NEW conclusion from grounds, while つまり adds no new information — it just says the same thing again. As for 〜というのは〜ことだ, that pattern is a proper frame for DEFINING terms, whereas つまり can flexibly slip into the middle of your speech whenever you need to "translate" your own point.
Examples
彼は母の弟です。つまり、私のおじです。
He is my mother's younger brother. In other words, he's my uncle.
来月から値段が上がります。つまり、今買ったほうが得だということです。
Prices will go up starting next month. In other words, it's better to buy now.
つまり、あなたは行きたくないということですね。
So in short, you don't want to go, right?