The principle of explosion is the law of classical logic and similar systems of logic, according to which any statement can be proven from a contradiction. Some early formal systems like Frege's Begriffsschrift contained hidden contradictions in the basic axioms, but the fundamental problem doesn't vanish even if the basic axioms are free from contradictions (=consistent). The problem is that it's all too easy for a human to make a mistake leading to a contradiction.
One strategy how this problem is addressed in everyday live is to be suspicious with respect to chains of reasoning which wander too far off from the topic at hand. This strategy could be called the relevance principle.
This problem also motivated the development of different systems of paraconsistent logic. It seems to me that relevance logic is one of these systems, even so I admit that its main goal is to avoid the paradoxes of material and strict implication. From the texts I read about relevance logic, I conclude that it's quite successful at formalizing the relevance principle (via the variable sharing principle). However, what I miss so far are investigations whether there are important and relevant theorems that can't be proved if the relevance principle is adopted.
What makes me uncomfortable about the relevance principle is that complex numbers can be used to prove some statements about natural numbers which can be very difficult to prove without them. So I wonder whether there exist good justifications for the relevance principle. However, this is also a more direct question about the existing systems of relevance logic and their propositional variable sharing principle. Their proof theory seems to be designed with the goal that implications violating the variable sharing principle can't be proved, without compromising the ability to prove implications satisfying the variable sharing principle.
However, I didn't find any indications whether these goal were achieved. Will I find such indications (or even proofs) if I read more thorough expositions of relevance logic, or is there something wrong with my expectations that such indications (or proofs) should be given?