までに is a combination of two different types of particles. The 副助詞（ふくじょし） (adverbial particle) まで, and the 格助詞（かくじょし） (case-marking particle) に. までに is verb similar to まで when it means ‘until’. However, there is one very important distinction. This distinction is that までに means ‘by’, not ‘until’.
To use までに, we will need to attach it to the end of a noun, or verb in the non-past form.

• 5時（じ）までに駅（えき）に来（き）てください。
  Please come to the station by 5 o’clock.
• 遊（あそ）びに行（い）くまでに片付（かたづ）けてね。
  Please tidy up by the time you go out to play.

To understand the difference between まで, and までに, we need to remember that に usually marks a ‘target’, or a ‘destination’ for where something will happen. In this case, まで is the ‘target’ that に is marking. This is due to the fact that まで means 'as far as' (まで is sometimes written using kanji 迄（まで）, especially in older/formal texts, and newspapers).

• 来月（らいげつ）までにレポートを書（か） く。
  I will write a report by next month. (Focus is on ‘next month’ being the deadline)
• 来月（らいげつ）までレポートを書（か）く。
  I am writing a report until next month. (Focus is on ‘next month’ being the end point for something that will continue until that point)

In this way, までに more literally means ‘(A) as far as (に marks the target), (B).