You can download the app directly on your device through its respective App Store or by using the following links:
Conversations allows emails to be grouped in threads. This lets you see an entire conversation between you and a friend and save a bit of time. You can turn off the conversations feature in the App's settings.
The redesigned interface makes it easier to get access to the features you use the most. Things you do all of the time like search, starring, and deleting are now one-click actions that appear when you hover over an email. Additionally the left hand toolbar can now be collapsed so you can use more of your display area.
The update also brings other new features which were previously reserved for premium Mail Plus users. Those features include disposable email addresses, enhanced filters and automatic message forwarding. Yahoo Mail users will now get 1TB (1000 GB) of free storage, which is a lot more than any of their competitors.
With the new update you also get themes which will appear across your browser, smartphone or tablet. When you Choose a new photo theme in one place, and it will apply across all your devices.
This new desktop experience is available in English in the US, Canada, UK, Philippines, Malaysia, India, Ireland, New Zealand and South Africa with more countries and languages coming soon.
source - Yahoo (Tumblr)
*Yahoo Mail for iOS has been updated to version 2.0
*Yahoo Mail for Android has been updated to version 3.0