What are Flask Blueprints, exactly?

A blueprint is a template for generating a "section" of a web application. You can think of it as a mold:

You can take the blueprint and apply it to your application in several places. Each time you apply it the blueprint will create a new version of its structure in the plaster of your application.

# An example
from flask import Blueprint

tree_mold = Blueprint("mold", __name__)

@tree_mold.route("/leaves")
def leaves():
    return "This tree has leaves"

@tree_mold.route("/roots")
def roots():
    return "And roots as well"

@tree_mold.route("/rings")
@tree_mold.route("/rings/<int:year>")
def rings(year=None):
    return "Looking at the rings for {year}".format(year=year)

This is a simple mold for working with trees - it says that any application that deals with trees should provide access to its leaves, its roots, and its rings (by year). By itself, it is a hollow shell - it cannot route, it cannot respond, until it is impressed upon an application:

from tree_workshop import tree_mold

app.register_blueprint(tree_mold, url_prefix="/oak")
app.register_blueprint(tree_mold, url_prefix="/fir")
app.register_blueprint(tree_mold, url_prefix="/ash")

Once it is created it may be "impressed" on the application by using the register_blueprint function - this "impresses" the mold of the blueprint on the application at the locations specified by url_prefix.

As pointed out in a comment by @Devasish, this article provides a good answer:

http://exploreflask.com/en/latest/blueprints.html

Quoting from the article:

An example of this would be Facebook. If Facebook used Flask, it might have blueprints for the static pages (i.e. signed-out home, register, about, etc.), the dashboard (i.e. the news feed), profiles (/robert/about and /robert/photos), settings (/settings/security and /settings/privacy) and many more. These components all share a general layout and styles, but each has its own layout as well

This is a very good interpretation, especially the part "if Facebook used Flask". It gives us a concrete situation to visualize how Blueprint actually works.