Origins
Strawberry jam and a nature reserve share the same Latin verb. Preserve comes from Late Latin praeservāre — prae- ('before') plus servāre ('to keep, to guard'). To preserve is to protect something before harm arrives.
Latin servāre produced one of the largest word families in English. Conserve means to 'keep together'. Reserve means to 'keep back'. Observe means to 'watch over' — guarding with the eyes. A servant is one who keeps and guards. Even deserve belongs: Latin dēservīre meant 'to serve devotedly', and the modern sense of earning something flows from the idea of faithful service.
The food sense appeared in the 16th century. Fruit preserves are fruit kept safe from decay through sugar. The method was ancient, but the English word for it was new — earlier cooks simply 'kept' or 'saved' their fruit.
Later History
Game preserves — tracts of land where hunting was restricted — date from the same period. A preserve was land 'guarded in advance' for the landowner's exclusive use. The word carried authority: to preserve something was to claim it.
The modern conservation movement adopted preserve deliberately. A nature preserve is land kept safe from development, echoing the original Latin promise: guard it now, before the damage is done.