The Kitzur Shulchan Aruch (6:1) tells us, “When one makes a berachah he should have in mind the meaning of the words.” Is there any halachic source (i.e. Kitzur Shulchan Aruch, Shulchan Aruch or Mishnah Berurah) that says when one davens he should know the meaning of the words?
Learn kuntres hateffilah from the Rebbe Rashab Z"L. It explains it in detail and it is not a very big maamar. Let me know if this helps.
There is a source which says that when one davens he need not know the meaning of the words.
The O Ch Mishna Berura 101  on the law about praying in any language says
“But in Hebrew, one performs one's obligation even if he does not understand the language”.
O Ch 101 speaks about the Amidah. The Shaar Hatziyun there refers to O Ch 62 which refers to the Shema.