The new challenges appear in the Club section of the app. As of writing there are three challenges to join, including a 15K February Weekly Challenge, a 50K March Weekly Challenge, and a 100K March Weekly Challenge. Tapping on one sends you to a summary screen that tells you how many runners are currently participating and how long the challenge runs for.
Tapping on the Join button enrolls you in the challenge, but you can leave it at any time through the challenge overflow menu (the three dots in the upper right corner of the screen). It also looks like you can only participate in challenges if your privacy setting is set to "Friends (social)" or "Everyone (public)".
Completing challenges earns users achievement badges, similar to those found in Apple's Activity app. In addition to the weekly challenges, Nike says there will also be occasional special Nike Challenges, which sound a lot like Apple's seasonal/one-off challenges that many Apple Watch users will be familiar with.
The Nike app's last major feature update came in October, when Nike introduced Audio Guided Runs to coincide with the launch of Apple Watch Series 3 models.
The Nike+ Run Club app can be downloaded on the iPhone and all Apple Watch models, but with Nike+ models, there's an option to launch the Nike+ Run Club app from the exclusive Nike watch faces.
Nike+ Run Club is available from the App Store for free. [Direct Link]