1.
sturdy, strong, durable
Able to withstand wear, pressure, or damage; not easily broken.
This bag is sturdier than it looks, and I've been using it for ten years.
Longer example showing durability over time
2.
healthy, robust
Having good health, not prone to illness.
丈夫 is a na-adjective: 丈夫な (before nouns), 丈夫だ/です (predicate). It can describe both objects (sturdy/durable) and people (healthy).
Note: 大丈夫 (all right, okay) is a related word. The kanji 丈 means 'length/height' and 夫 means 'man' - originally referring to a grown, strong man.