I wanted to add a different interpretation of the question:
The Singularity is also referred to in most science fiction as the point in which the human brain is able to be fully compiled by a machine. Some only link this event to it’s outcome [e.g. the singularity is when artificial intelligence meets or exceeds human cognition; or when your thoughts/dreams/memories can be recorded; or you can download a book to your brain to learn a new language, etc]. The implications are always intriguing to explore, especially via your western hollywood rendition [Johnny Mnemonic; The Matrix; I, Robot; Her, Ghost in the Shell (original anime); etc.]
The other interpretation posted is more like explaining the conservation of mass… it’s close, and accurate, but doesn’t answer the question. For other information, a singularity is also what scientists theorize is at the center of black holes, or rather, what they USED to think. There is still debate about whether the center of a black hole is a singularity that compiles all atoms sucked in until it reaches critical mass and supernovas like a star, or if the black hole reduces down to mathematical zero, but is still technically a single atom-wide hole that all the matter passes through as it’s spit outside the other side of the space-time plane.
ELI5 TL;DR – The Singularity is the fantasy of two units of matter physically occupying the same space-time; as well as the other more common reference to when you can back up your brain to a microsd card.
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