Fulton and Macpherson suggests the way to compactify the set of $n$-labelled distinct point on variety in their paper, "[A Compactification of Configuration Spaces][1]"

In this paper, the process and the motivation is very simple, and hence the construction itself is not that hard to understand.

However, I couldn't check the motivation of $X[n]^+$. In the paper, it is for describing $n$-th degenerated configuration of $X$. In what sense, the fiber of $X[n]^+ \to X[n]$ becomes such a configuration? I tried to understand this by letting $X = \mathbb{P}^1$, but still don't know unified description of whole phenomenon.



  [1]: https://www.jstor.org/stable/2946631