A choke point forces attackers to use a narrow channel, which you can monitor and control. There are probably many examples of choke points in your life: the toll booth on a bridge, the check-out line at the supermarket, the ticket booth at a movie theatre.
In network security, the firewall between your site and the Internet (assuming that it's the only connection between your site and the Internet) is such a choke point; anyone who's going to attack your site from the Internet is going to have to come through that channel, which should be defended against such attacks. You should be watching carefully for such attacks and be prepared to respond if you see them.
A choke point is useless if there's an effective way for an attacker to go around it. Why bother attacking the fortified front door if the kitchen door around back is wide open? Similarly, from a network security point of view, why bother attacking the firewall if there are dozens or hundreds of unsecured dial-up lines that could be attacked more easily and probably more successfully?
A second Internet connection - even an indirect one, like a connection to another company which has its own Internet connection elsewhere - is an even more threatening breach. Internet-based attackers might not have a modem available, or might not have gotten around to acquiring phone service they don't need to pay for, but they can certainly find even roundabout Internet connections to your site.
A choke point may seem to be putting all your eggs in one basket, and therefore a bad idea, but the key is that it's a basket you can guard carefully. The alternative is to split your attention among many different possible avenues of attack. If you split your attention in this way, chances are that you won't be able to do an adequate job of defending any of the avenues of attack, or that someone will slip through one while you're busy defending another (where they may even have staged a diversion specifically to draw your attention away from their real attack).