A number has ascending digits when each digit is strictly greater than the one before it — the digits climb like a staircase: 123, 1359, 2589, 13578.
Because the digits must be distinct and increasing, every such number is just a chosen subset of the digits 1–9 written in order (0 can't appear — it would have to lead). That makes them surprisingly scarce: there are only 466 numbers of any size with three or more strictly ascending digits (and just 502 of every length combined). The longest possible is 123456789.
Ascending-digit numbers are a favourite in recreational mathematics and often turn up as memorable PINs, addresses, and dates.