Final answer:
ABBA won the 1974 Eurovision Song Contest with their song 'Waterloo', which led them to international success.
Step-by-step explanation:
The band that won the 1974 Eurovision Song Contest was ABBA, a Swedish pop group.
With their hit song 'Waterloo', they not only won the contest but also gained international fame, marking the beginning of a highly successful career in the music industry.
The song 'Waterloo' is known for its catchy tune and distinctive performance, which ultimately helped ABBA secure their place in pop music history.