As Brian noted, Vespers is part of the Divine Office, which is a type of prayer that dates back to the very first centuries of Christianity. This prayer started in monasteries, who strived to lived by Paul's exortation to "pray without ceasing".
It is rooted in the psalms, which as you know as songs of praise to the Lord. Early desert fathers tended to be literalists, and thus tried to literally pray the psalms without ceasing, 24 hours/day, but found it to interfer with other human needs, like eating and sleeping. Since that time, this type of prayer has evolved into 'partitions', broken up throughout the day.
All monasteries today say the Divine Office (most still chant them). Listed below is a commom daily schedule for monasteries. As you can see, the Divine Office is deeply integrated into the monks daily life (bolded mine);
Rise:
4:50 a.m.
Matins:
5:15
Lauds:
6:15
Low Mass:
6:50
Prime:
8:00
Lectio Divina:
9:00
Terce, High Mass:
10:00
Study or Work:
11:15
Sext:
12:50 p.m.
Recreation:
2:00
None:
2:35
Manual Labor:
3:00
Vespers:
6:00
Silent Prayer:
6:30
Lectio Divina or Conference:
7:00
Compline:
8:25