Of course I'm speaking in generalities. I would have hoped it was obvious that I'm not allowed to disclose information I receive in the course of confidential briefings from police officers or members of the security services. I'd lose my job, at least.
If you would like a concrete example, then think back to 2005. Prior to the bombings on the Tube, the attackers carried out a rehearsal of their actions, making the journeys as they would on the day, going through the motions if you will. Without blaming anyone, that was a missed opportunity to stop the attacks which took place nine days later.
Or consider Manchester last year, where we now know that the individual who carried out that attack was behaving suspiciously in and around the city centre for some hours prior. Again, an opportunity missed.
Now it may be the case that in those specific incidents the attackers did nothing which gave anyone cause for concern, hence the alarm was never raised. However, other attacks have been stopped at the reconaisance/rehearsal stage, or shortly after, precisely because of suspicious behaviour being highlighted by members of the public.
Most terrorists are no more intelligent than you, or I, and many a damn sight less so. Like all criminals, they make mistakes and do things which betray them to others, even if only in very small ways. The aim of "See It, Say It" is to encourage people to report those small concerns when they come to light because what may seem a tiny, inconsequential piece of information to you could just be a vital piece in the overall jigsaw when added to other facts in the security services' possession.
(Note: I've used 7/7 and Manchester Areana as examples because they are already in the public domain, not because I think mistakes were made by anyone in either case. Indeed, I am aware of lessons which have been learned from both of these attacks which inform current policy.)