The definite article "the" is used when the reader should know which instance of that object you are talking about. In your example, the object is an estimation --- specifically, the "more accurate estimation" described in the previous sentence. In this case, "the more" only works in the second sentence because the object is introduced in the first sentence.
"The" is not added only to "more" in your example. It's added to the whole noun phrase: "the more accurate estimation".
Here's a similar sentence that avoids the word "more" completely but uses "the":
This calculation method produces accurate results. The results it produces can be used in variety of applications
In this case, it's "the results," which is equivalent to "the more accurate estimation" in your example
"The" can also be used when something is countable or measurable (that reference has good examples of when a certain noun is countable or not).
"More" can mean "an amount larger than expected" or "an amount larger than before" (see the definition in Macmillan dictionary), so while it may not refer to a specific number, it can refer to something measurable.
The more I talk to you, the more I like you!
She didn't know what to do on a plane her first time, but the more she traveled, the more she learned