First, I don't believe that "why" is something that this community can answer; this was a decision of the designers and their reasons, to the extent that they have any, are a mystery.

Notwithstanding, your question is why the XP per level looks like this:

![XP per level][1]

Steady growth until 11th level, then a sharp drop and not reaching the 10->11 level again until 14->15.

However, the XP values are only one side of the equation; the other is how much XP is gained per encounter (p.82 DMG). Ignoring modifiers, by combining these you get this chart:

![Encounters per Level][2]

Easy, Hard and Deadly encounters are **approximately** 2/3, 1.5 and 3 times a Medium encounter (presumably because of rounding off). Focusing just on the "Medium" encounters (which should be the bulk of encounters) it can be seen that you need 6 to reach levels 2 and 3, 12 to reach 4, approximately 15 for levels 5 through 10, 17 for level 11 and then about 9 to 10 for levels 12 to 20.

However, due to the strange way that XP budgets do not equate with XP awarded, you will only have this number of encounters if *every* encounter is with a single monster. If your encounters are typically with 3-6 creatures (most of mine are) then you will need *twice* as many encounters to get the same number of XP.

In this context, the jump at level 11 is only about 10% and then it falls to a much lower and **approximately** constant value.

If I were to speculate, and I will, I would guess that the design intent is to:

 - Provide relatively rapid advancement through the early levels.
 - Slow down this advancement in the mid-levels (4-11) to an approximately constant level of about 15 medium/10 hard encounters (noting that difficulty factors will make the *actual* number of encounters 2-3 times this).
 - Provide more rapid advancement (about 1/3 quicker) for the levels 12-20.

This accelerates the PCs through the fragile early stages and provides rapid gratification, provides a long period of play in the mid-levels, suitable for the dungeon-grind and then move more quickly through the levels where nation and world shaking events may be happening.
  [1]: https://i.sstatic.net/ezsDF.png
  [2]: https://i.sstatic.net/BoTgI.png