An ascension streak is a consecutive sequence of ascended games. A player must be able to win reliably to get a long streak. Therefore, streaks are a coveted display of player skill (along with (unofficial) conducts and speed runs). Only 9.6% of all winning accounts on NAO have a streak of three or more ascensions.
There is nothing special about the individual games. Perhaps except that some people become more risk averse when they are close to a personal record.