The idea that numbers have a character is Pythagorean: in the school at Croton, in the sixth century BC, one was the origin, two the split, three the harmony that puts it back together. From there numerology passed through kabbalah and the Renaissance, and resurfaced in the 1990s in the form we know today — repeated sequences spotted on clocks, licence plates, receipts — with the books of Doreen Virtue.
The basic rule is reduction: add the digits until one is left, so 1987 becomes 25 and then 7. The exceptions are the master numbers — 11, 22, 33 — which by convention are not reduced, since they count as an amplified version of the digit behind them. Triples like 111 or 444 read the same digit three times, that is, with emphasis; sequences like 1234 or 1212 read instead as movement, a direction rather than a fixed point.
It is worth saying: the reason a number seems to follow you around has a name, the frequency illusion. Once a sequence has caught your eye, the brain starts noticing it everywhere and quietly discards every time it was absent. That does not make the exercise pointless, though — if a number sticks with you it is usually because you were already thinking about something, and reading its meaning is a way of naming it.