You would do some kind of join between the the two tables and select entries from the join. A simple cartesian join can be achieved by comma-separating the tables you are querying from.
create table holidays (
name text not null,
fromdate text not null,
todate text not null
);
create table appointments (
name text not null,
date text not null
);
insert into holidays values ('Christmas Holiday', '2014-12-05', '2014-12-24');
insert into appointments values ('Dentist', '2014-11-06');
insert into appointments values ('Doctor', '2014-12-06');
select h.name, a.name, a.date
from appointments a, holidays h
where a.date between h.fromdate and h.todate;