Notation: What does this summation mean?

I think it should be written as

$$\sum_{1\leq i < j \leq N} {d_{ij}}. $$

This way, it's clear that you sum over all $i,j$ satisfying the inequality $1\leq i < j \leq N$.

If $N=5$, this is equal to

$$d_{12} + d_{13} + d_{14} + d_{15} + d_{23} + d_{24} + d_{25} + d_{34} + d_{35} + d_{45}.$$

It's shorthand for $$ \sum_{j=1}^N \sum_{i=1}^{j-1}d_{ij}$$

$d_{12}+d_{13}+d_{14}+d_{15}+d_{23}+d_{24}+d_{25}+d_{34}+d_{35}+d_{45}$