The most common and most likely answer to this crossword clue is the 10 letter word CARTWHEELS
I've seen this crossword clue in Financial Times
C
A
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T
W
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Buddy explains!
The straight part
We know that "Were they vitally important to the agricultural revolution" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case were they vitally important to the agricultural revolution = cartwheels.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CARTWHEELS mean?
CARTWHEELS noun- The literal wheel of a cart.
- A gymnastic maneuver whereby the gymnast rotates to one side or the other while keeping arms and legs outstretched, spinning for one or more revolutions.
- A crown coin; its value, 5 shillings.
- A silver dollar of the larger size produced before 1979.
- To perform the gymnastics feat of a cartwheel.
- To flip end over end: normally said of a crashing vehicle or aircraft.