Often, when the Vatican speaks, it can be a fairly one-sided conversation, issuing encyclicals and other formal documents stating the Roman Catholic Church’s official position on doctrine or other matters. 
But Pope Francis, who has already shaken up the Vatican, is asking the world’s one billion Catholics for their opinions on a questionnaire covering social issues like same-sex marriage, cohabitation by unwed couples, contraception, and the place of divorced and remarried people in the church.
and ends:

“It’s a matter of communicating, which is what we do every day,” he said. “The bishops need the people’s opinion and our interpretation of the doctrine.”
 and in the middle:

“It really responds to the desire for the people, the laity in the church, to be consulted on matters which concern them so deeply,” Bishop Hine told Vatican Radio. “Couples are delighted that they’re going to be involved in the consultations.”
In the National Catholic Reporter piece on the same topic, which the NYTimes references, but obviously didn't read, it seems to be the case that some bishops will use polling to collect the data requested, and some collect the data in other ways:

While Baldisseri asks in his letter for wide consultation on the questions, an accompanying letter sent with the U.S. version of the Vatican document does not request the American bishops undertake wide consultation in their dioceses.
and the National Catholic Reporter makes it sound like this process is much less usual than the NYTimes did:

In an email after initial publication of this story, Osman said the bishops will follow a "usual process" for soliciting information as "Rome asks for this kind of consultation on a regular basis." 
Basically, the NYTimes piece made it sound as if the Vatican was requesting individual feedback about the doctrines of the Church from all the Catholics, possibly in advance of some big later change:

This time, however, some analysts say, the style and content of the questionnaire represent a deliberate effort by Francis to engage ordinary Catholics, unlike in the past when synods have attracted little attention. Francis has also raised expectations by changing the format, with next year’s meeting framed as a prelude to a second synod in 2015 that could bring proposed changes, even if few expect him to pursue major doctrinal shifts.
But when you look at the questionnaire itself, you get a different idea entirely--it's attempting to gather information about how Catholicism is actually being practiced: Do people understand the Church's teachings? Do they follow them? How does pastoral care work in the midst of an often blatant disregard for the Church's teachings?