The phrase can imply important life events or changes typically experienced during this age range. Many of my friends started families in their thirties.
Pro Tip 2/3
Subtle Nuances
Terms like 'early', 'mid', or 'late' help specify more precisely within the decade. He switched careers in his early thirties.
Pro Tip 3/3
Informal Planning
Used informally when talking about future plans without a specific age in mind. I plan to start my own business in my thirties.