It's a tricky term, but the definition given towards the top where "age-adjusted" is clickable helps clarify. It's introduced in "But an aging population only partially explains the rise in these deaths. Deaths by falls have risen 2.4-fold on an age-<adjusted basis>. " The <clickable> part in brackets (easy to miss) expands to:

> Age-adjusted data helps to compare health data over time or between groups more fairly by accounting for the age differences in populations. For example, suppose Population A has a higher average age than Population B. In that case, age-adjusting ensures that Population A's naturally higher death rate due to age doesn't skew comparisons of overall health between the two. This measurement makes death statistic comparisons more accurate than crude death rates.

An "age group" might be "45-54" or "85+" but a "population" would be "all age groups in 2000" or "all age groups in 2023". Age-adjusted here means the differences in the number of people in each population (2000 vs 2023) are normalized to each so we can compare the absolute numbers from each age group directly, not the other way around.

There is some immediate follow-up text which helps clarify they do not mean to normalize the age groups themselves together within a single population for comparison:

> While they [population age-adjusted fall deaths] have fallen among younger people and only risen slightly among the middle aged, they have risen substantially within every age bracket of the elderly.

This all gave me flashbacks to stats class, and I now need to go relax :).