CPI can lead to price changes in the forex in a couple of ways. First, like all announcements, if CPI misses or exceeds expectations the market for the USD will respond to it immediately. Which direction that movement will take is uncertain and it can lead to a lot of whipsaws or a lot of big price moves up and down. This is problematic for short term traders but can create some nice profits for forex dealers (including the interbank dealing desks) as traders move in and out of their positions after being stopped out. Fortunately CPI can be predictive for the trend in the longer term.
CPI's long term predictability partially rests on the normal cycle of economic growth. Economic growth leads to higher wages/employment/spending which leads to higher interest rates and yields which leads to a more valuable USD. In the video I have a couple of good examples of how a faster positive rate of change in CPI lead to exactly these kinds of trends. As we know, however, this relationship breaks down when the economy is contracting at the same time that the oil market is experiencing price shocks. This doesn't mean that inflation analysis is useless during those periods it just means that the same information has to be used differently.
During these periods, the Fed will have a very difficult time trying to manage their inflation target because the normal tools of monetary policy will only make the problem worse. During these periods it seems likely that a decline in the USD is unavoidable. Knowing the likely trend is helpful as you plan trades and this kind of simplified trend-based approach to inflation data can help cut through the inherent problems of the release.