Yes. To see how many steps you've walked today, tap on the Stats screen in the Navigation bar at the bottom of the screen. On the next screen, there will be a Yellow Blade that tracks Activity data. Your current step count will be displayed here.
Spire has multiple sensors inside the device that detects when you're walking. If you start walking and take at least 40 steps per minute for more than 2 minutes, Spire will set you in an Activity streak.
You can also see how much time you spent being active, which is yet another better indicator than just steps alone.