つまり

In other words

つまり is an expression that is used to reword existing information. 
This is usually used to sum up a conversation, but may be used to rephrase a statement.
It is typically used for confirmation.
 
Weblio distinguishes these as “in the end” and “rephrase” usages. 
つまり frequently uses のだ (explain or interrogate) and/or ね (Confirm)

A more formal/literary version of つまり is すなわち
A more objective version is ようするに (The gist of)

Examples

• つまり、まだ終わっていないんだね
  In other words, its not finished yet. 
  
  
• 自業自得、つまり、自分がやったことのせいだ。
  You reap what you sow, in other words its because of what you did. 
  
  
• 一日中調べていた。つまり、彼は頑張っているんだ
  He researched it all day. In other words, he’s trying hard. 
  
  

Conversation Example

• 君が勉強しなかったから不合格だね。
  You failed because you didn’t study.
  つまり自業自得だ。
  In other words, its your own fault.
  
  
• 今はちょっと忙しい。。
  I’m a little busy right now..
  つまり、できないんだね
  In other words, you can’t do it right.