Some people say the Trinity—the idea that there is one God Who subsists in three fully distinct but fully divine persons—doesn’t make sense. This depends entirely on what one means by the concept of making “sense.”
If one means that the Trinity is irrational, that it violates some law of reason, then the challenge is simply false. There is no violation of the laws of reason in the Trinity. Anyone who thinks I’m mistaken on this point must identify the specific law being breached in light of the orthodox teaching on the Trinity (as opposed to some misrepresentation; we don’t believe in three gods, for example).
One might argue that the Trinity doesn’t make sense in that it doesn’t appeal to any sense perception, that it’s hard to conceptualize the Trinity because it can’t be pictured in the mind. This seems accurate, but it’s hardly relevant. Individual spiritual beings—God, angels, souls—can’t be pictured. Though they may manifest themselves in physical form (we find this in the Bible), this is not what they actually look like. Even so, the concepts are certainly intelligible.
The same is true with immaterial things like love, kindness, or vengeance. Each of these may be evidenced in actions that can be seen, but they are not themselves physical, and indeed no accurate physical characterization or “sense” of them can even be imagined.
So, it is no liability that no one can picture the Trinity. It is not “sensible” in that way. This tells you nothing about the truth of the doctrine. That question is answered by a different means: Does God’s own self-revelation give us reason to believe that the doctrine of the Trinity, classically understood, is an accurate and true description, as far as it goes, of God’s nature? The answer to that is clearly yes.