Apparently, some people have a problem with this expression. I don’t.
When we say that a person or thing is “very unique”, the rigidly inflexible among us might complain that “unique” means one-of-a-kind, and that it is impossible to be more or less one-of-a-kind. Either a thing is unique or there is another like it.
I have some sympathy for this approach in the context of mathematical proofs, where exact sameness is possible.
However, in the context of the real world and of everyday speech, the truth is that all things in heaven and earth are unique. No two snowflakes are alike, but neither are any two oranges, motor boats, or life philosophies. The perfect, mathematical meaning of uniqueness is useless here, since if everything is unique, the word carries no information content. So in the context of everyday conversation, something tends to be described as unique when it stands out from prevailing norms in a significant way.
Every experience is unique. No two trips to the grocery store go exactly the same. But the phrase “unique experience” tends to refer to things like fainting while giving a performance, or turning around and finding a bear inches from your face. And if that performance is in a sex dungeon, or if that bear then starts whistling the national anthem, I would say that qualifies the experience as “more unique”, perhaps even “very unique”.
Let’s face it: uniqueness, in the real world, comes in gradations.
Edit: Upon further thought, there are ways in which the mathematical usage does find a home in everyday speech. For example: “She was unique among her peers in having a professional football player for a father.” In this case, the parameters for uniqueness are carefully set down. The set of people in her peer group whose father is a professional football player has one member, namely her. She could not be more or less or especially unique in this respect. However, when the metric for uniqueness is not so carefully laid out (as it is frequently not), uniqueness ceases to be simply an on/off switch.