It is an interesting question, let me define (not necessary true) some definitions before my discussion.
1) Explanation: Suppose a statement S is true, then "explanation" is by means of person A applies human semantic language (for example: Platonic dialectic argument) and/or symbolic language (for example: math and physics) to convince person B believes that statement S is true.
2) Belief: Belief is a state of human mind in which person A thinks something to be the case with or without empirical justification and scientific reasoning.
3) Information: Information is a set of data, knowledge and beliefs. Note that, wrong information is still belongs to information.
4) Agnosticism: There exists something that is unknowable for human being. For examples, samsara, reincarnation, divine are still under debating, no satisfactorily determination is found.
5) Fallibilism: An epistemological view that nothing can be rationally supported or justified in a conclusive way.
So, in order to explain anything, say "table", inevitably we need to use certain steps inform of semantic or symbolic language such that you belief that this is really a "table", provided that we have already the concept of "table" by a priori or by a posteriori approach. If we replace the material "table" with a immaterial "red", for one who doesn't have the concept of "red" will not able to understand any explanation of the perception, "red". To reduce the semantic complication, suppose everyone know that "red" is kind of light within certain range of wavelength, for instance, any light which has wavelength between 650-700 nano-meter is define as "red", someone will then ask what "light" is? Then another may answer light is kind of electromagnetic radiation (EMR); then what is EMR? EMR is certain components of electric waves and magnetic waves; then what is electric wave? ...
So, if we keep asking the question backward further and further, then in philosophy, we are involved in so called "regress problem" or "Münchhausen trilemma". The consequence will be as follow:
a) Until certain points, we reject to explain further. In this case, EMR with the wavelength between 650-700 nm is my final explanation of "red".
b) Or the explanation will go backward with an infinite chain. That is A because of B, B because of C, and C because of D ...; provided that we have infinite many true information A, B, C, D...
c) Or the explanation is cyclic with a circular reasoning. That is A because of B, B because of C, and C because of A.
So, if someone explains "red" in form of the above a), b), or c), then I should believe that this explanation is true under my belief. That is, this explanation is consistent with the state of my mind and my previous knowledge (the term knowledge need to be defined).
However, the above discussion is not even close to the answer of your question "Is there anything that can't be explained?" Your question is more complicated than one thought. Let reduce your question to "is there something can be explained?” Obviously (before I study philosophy), I believe that 3+3=6, for instance, three apples plus three apples is six apples, and hence 3+3=6. But my explaination is cannot be hold for much genius, because I accidentally apply the ontology, while the number "3" may not have something attach with (I attach the 3 with the apple). Moreover, we even don't know whether "3" is an abstract object or not, more worse is that, we even don't whether abstract object exist or not. (May search the Fregean argument of mathematics Platonism)
If we rooted on the skepticism, fallibilism or agnosticism, then nothing can be explained. One of the reasons is that all human argument is based on semantic language and, unfortunately, semantic language is only a tiny part of the universal, part cannot cover the whole. That is why human consciousness and supernatural power are hard to be explained by semantic approach.
Regard to the day-to-day practice, 3+3=6 can be explained satisfactory. Likewise, "table" and "red" can also be explained satisfactory provided that we don't asked too many questions backward. According to the determinism, everything is causally determinate by some reasoning, and hence "free will" is only by chance but not by necessity.
Short closing: In day-to-day real life, all events can be explained, if not now, then in the future.
In the essential natural events, nothing can be explained by using semantic approach only, especially by human-to-human argument. Note that, truth is existed before everything and, it is independent on the observer and explanation.