Origins
To reserve is to hold something back, and the word itself has been held in careful use since the 14th century. It comes from Latin reservāre, composed of re- ('back') and servāre ('to keep, to save, to guard').
The Latin servāre descends from Proto-Indo-European *ser-, meaning 'to protect' or 'to watch over'. This root generated one of the most productive word families in English. To conserve is to keep things together. To preserve is to guard something in advance. To observe is to watch over carefully. A servant is one who guards and attends.
The noun reserve appeared in the 17th century with a military sense — troops held back from the front line, ready if needed. Nature reserves followed the same logic: land withdrawn from ordinary use and held in protection.
Later History
Reservoir comes from the same family, via French — a place where water is kept back. Even the personality trait of being reserved traces this etymology: a reserved person holds themselves back, guarding their thoughts from public view.
The word's journey from 'to guard' to 'to book a table' is a quiet narrowing. What was once an act of protection became an act of scheduling — though booking a restaurant table is, in a small way, guarding your place.