Well, I can't say this is an easy question. I just use this word and may never think about its meaning if you didn't ask. :)
When "mà" stands at the end of a sentence, it has explaining function.
A: Sao anh không đi làm? - Why don't you go to work?
B: Hôm nay là chủ nhật mà. - It's Sunday today. (that's why I don't need to work)
When something happens like what somebody predicted or warned before, then he/she uses "mà" to emphasize what he already predicted/warned.
A: Con bị cảm lạnh rồi. - I've caught a cold.
B: Mẹ đã bảo rồi mà. Đáng lẽ con phải mặc áo ấm trước khi ra ngoài chứ. - I told you already. You should have dressed warmly before going out.
Peter nói: "Tớ biết mà!" - "I knew it!", said Peter.
Hope this helps.