It implies that foreigners need to be able to identify themselves and show their residence permits, border ingress stamps or other proof of them being in the country legally. In this sense it can be compared to the visa waiver which non-Americans from eligible countries needed to sign before crossing the US border. It contained questions in the line of 'Are you entering the US to commit crimes' and 'Were you active in the Nazi-party in Germany from 1932-1945'. While no criminal worth her salt would answer the former question with 'yes', it did give an additional legal handle to expel her should she be caught, as well as legal grounds to deny her access the next time she tried to enter the US.
This is not possible with 'open borders' as the police and 'border guard' have a very limited mandate to check on what they deem to be suspect individuals.
Back when I was a small boy, almost every month there was some bombing going on in Israel. These attacks have been greatly reduced by several measures, including the building of the wall.
As for the second par of your argument, I don't know the context but to me it seems more of a correlation than a causation.
I cross every day the border. Twice a week, I cross another border which is meant to be closed from 19h to 6h (many small borders near the FR-CH do that). There is a simply locked barrier. Nothing more. This has been here for 25+ years. Of course, I've crossed "illegally" this border by bike plenty of times (its faster) and it has been very very easy (I won't even talk about all the woods around the border that haven't got a single fence). A terrorist wanting to cross a border would be very stupid to get caught.
So all this talk about how getting out of the EU is complete bullshit to me.