Here's how it works: On Google's home page, click on the microphone in the search edit box and speak your query. That, in and of itself, is not new. That feature was rolled out by Google two years ago. What is new, though, is that Chrome will now speak back to you, in a manner similar to how the Google Search app works on Android or iOS.
In addition, once you speak, you’ll see your query appear -- assuming, of course, it's understood.
Sometimes, particularly with searches that are easy to answer -- such as "How old is U.S. President Barack Obama," the results will be include a direct answer (an information card, per Google Now terminology). In that case, the answer is (of course), 51.
What's far more impressive, though, is that you can continue the "search conversation" from that point. For example, you could then ask the query, "How tall is he?" Notice that you are not saying "How tall is Barack Obama?" but rather "How tall is he," using a pronoun.
Using a voice query, you'll see the result: 6'1" (Barack Obama, height).
Further questions such as "Who is his wife" will continue to conversation.
If you want to try it out, ensure that you have the correct version -- 27.0.1453.93 or later. If you don't, open your Chrome browser settings, and click the About menu item. Chrome will both tell you the current version and check for an update. If an update is available -- it may even tell you it's downloaded an update and you just need to restart the browser -- it will download it and ask you to restart the browser.
Once Chrome restarts, you can head to www.google.com and click the microphone in the search box to try it out yourself.