reputation; public estimation
Archaic expression for how one is regarded by society; not used in modern Japanese outside historical or literary contexts.
昔の武士にとって、世の覚えは命よりも重かった。
For samurai of old, their reputation in society was heavier than life itself.
The phrase combines 世 (world, society) and 覚え (memory, recognition), literally 'society's memory/recognition'. The exact historical derivation is uncertain, but it reflects an older way of expressing social standing.