verb
BAD : We've reserved the school hall for the evening.
GOOD : We've booked the school hall for the evening.
BAD : I've finally managed to reserve a two-room house on the beach.
GOOD : I've finally managed to book a two-room house on the beach.
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reserve (or book ) = arrange for a seat on a train, a seat in a theatre, a table in a restaurant etc, to be kept for you to use at a certain time: 'I'd like to reserve two seats in the front row for tomorrow night's performance.'
book = (British English) arrange for a hotel room, holiday accommodation etc, to be kept for you to use at a certain time: 'We've booked a holiday cottage in the Lake District for the first two weeks in June.' Note that in American English the usual word for this meaning is reserve .