What is Considered an "Older" Home?

I distinctly remember during our home-buying journey when our real estate agent asked if we wanted new construction, something close to it, or if we'd be open to an "older" home. When we said yes, we knew that--in our budget--we would likely be looking at a few houses built in the early-to-mid 1900s. However, if we'd had a much larger budget, we could very well have wound up walking through (and legitimately considering) houses built in the early 1800s.