Mainstream modern Western culture is largely disinterested in the "big questions". Our civilization's answer to the question of why we are here is "don't think about it too much. We should attempt to answer this question, even if we do not expect to make any novel progress. Asking certain questions is valuable even if we do not expect to produce answers for them.
What does it signify when we say that something has a "meaning"? There is a narrow sense which many people learn in school. You may have analysed a poem, book or a movie. This movie is (apparently) one big analogy to World War 2, and the "meaning" of the movie is that war is bad or something. The art ostensibly exists to express this one idea, and through the use of simple metaphor is able to convey the idea more subtly. This, according to the analyst, is more effective than the idea being stated outright (which I do not entirely agree with either). If this simple meaning can be said of a piece of art, either the critic does not know what they are talking about or the art is not very good.
True art cannot be summarised in this way. What is the meaning of Slaughterhouse Five by Kurt Vonnegut? It is about World War 2, and that war is bad, but it is also about the non-linearity of subjective time. In its absurdity, Slaughterhouse Five demonstrates how absurd the actual true events of World War 2 were. Slaughterhouse Five is about the futile attempt to reconcile the events of actual human lives, which are chaotic and messy do not follow the arc of neat fairy tales. I could say more about Slaughterhouse Five, but I will stop myself.
I had this same experience while playing the video game The Witness. At the most basic level of interpretation this game is about non-verbal puzzle solving. It is also about perception and the ability to recognise patterns in the world. It is also about beauty and loss in ways that are hard to explain. I had been playing this game thinking that I am extremely smart, only to realise that the only reason I had thought to even look for puzzles in the game is because I knew that someone had put them there for me to find. This epiphany was the closest I had come to having my agnostic/atheist worldview challenged for many years. Maybe it is pathetic to have had what amounts to a "religious experience" in a video game, but it happened nonetheless.
The final example I have is the book Infinite Jest by David Wallace. I could not even begin to describe what this book is about. The book has a setting and a plot, which would take some time to explain, but explaining these surface details would not actually communicate the significance of this book. This book is sad, funny and disturbing all at once.
To summarise: I think that life has meaning, and that this meaning is akin to the meaning in great art; precisely the art which escapes our ability to describe it. Perhaps that is a round-about way to say that language is not enough to describe the meaning of life?