The riddle
If April Showers Bring May Flowers, What Do May Flowers Bring?
What the saying means
"April showers bring May flowers" says that rain in April is what makes plants bloom a month later. Wikipedia's article on the saying gives 1610 as the earliest known form, a poem line that reads "Sweet April showers / Do spring May flowers", and dates the longer version about March winds to 1886. The riddle takes the saying's pattern, one thing bringing another, and asks for the next link in the chain.
A ship with a flower in its name
The answer depends on a name. The Mayflower was an English merchant sailing ship with three masts. Wikipedia reports that it left Plymouth, England, on 16 September 1620, carrying 102 passengers and a crew of 25 to 30, which makes about 130 people on board. Pilgrims is the name given to the English settlers who founded the town of Plymouth, Massachusetts, and the ship is the best known thing about them. A May flower brings the ship, and the ship brings the Pilgrims.
Sixty-six days at sea
The Mayflower was headed for the Colony of Virginia but reached Cape Cod, Massachusetts, where the crew sighted land on 19 November 1620 and anchored two days later. From 16 September to 21 November is 66 days, which the article describes as about ten weeks at sea.
One letter and one sound apart
Spoken aloud, "May flowers" and Mayflower differ only by a faint z at the end. On paper the capital M and the single word mark the ship, but in speech nothing does, so the listener has to hear the ship inside the flowers. The answer lands best when it follows the question without a pause.