from the article:
> The Communications Data Bill would have given police and security services access, without a warrant, to details of all online communication in the UK - such as the time, duration, originator and recipient, and the location of the device from which it was made
So the addition of a warrant is new.
I would imagine it could work something like Ads in Gmail. A person from Google doesn't actually read your emails, but automated software does. It can then serve an ad based on the contents of your email, without (in theory) your privacy being intruded upon.
In a similar way, a Government "snooping system" could monitor everybody's electronic communications for patterns of suspicious activity. If it detected them, it could inform humans who could then apply for a warrant to open up the communication. In this way, everybody's communications would be monitored, but nobody's privacy would be breached without a warrant.