How does neural network solve XOR problem
Notice that the first table (orange line) is performing an OR operation and the second table (blue line) is performing an AND operation. XOR can be defined as (x OR y) AND NOT (x AND y) or $(x \lor y) \land \lnot (x \land y)$, so in other words: orange should fire and blue shouldn't fire. If we now look at this figure from your tutorial:



we can see that the weight of blue in the second layer is negative and small enough (more negative) such that the output can never fire if blue fires, i.e. the output can't fire if both inputs are firing.

$0 + 0 \ngtr 1 : \emptyset $ shouldn't fire  

$-2 + 0 \ngtr 1 : (x \land y) = T$ shouldn't fire  

$0 + 1.1 \gt 1 : (x \lor y) \land \lnot (x \land y) = T$ should fire  

$-2 + 1.1 \ngtr 1 : (x \land y) \land (x \lor y) = T$ shouldn't fire