Strength training causally improves muscle strength and daily functioning in older adults. Combined with balance exercises, it reduces fall incidents by approximately one third. Large population studies show a consistent association with lower cardiovascular mortality, although causality for that has not been proven.
Strength training is one of the few things we know with a high degree of certainty actually works: multiple well-designed studies show that it meaningfully improves muscle strength and day-to-day functioning in older adults, from climbing stairs to getting up from a chair. That effect is causal, not coincidental. Muscle mass itself grows less impressively than strength does, but for what you notice in daily life, the strength gain is what counts.
Preventing falls works best when you combine strength training with balance exercises. Lifting weights alone does not produce the same result. A combined programme shows a reduction of roughly one third in research. That is a concrete argument for choosing a programme at a gym or physiotherapist that includes both elements, rather than purely machines or free weights.
On lifespan: people who strength train regularly have a lower risk of dying from cardiovascular disease and from other causes in large population studies. This is not a proven causal relationship, since healthier people also tend to be more active, but the association is consistent enough to factor in. The optimal frequency and load have not been precisely established, so do not worry about finding the perfect formula: working all the major muscle groups twice a week with sufficient resistance is a realistic and defensible starting point.
Overview across multiple factors (3 research records, 5 sources). The strength of the evidence differs by component -- read the answer for the nuance.