From wikipedia: Boundary value problem - Wikipedia, the free encyclopedia
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional restraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions.
My interpretation: Differential equations are a way of modeling complicated systems. Something as simple as a second-order, linear, differential equation, is capable of modeling just about anything that classical physics throws at you, mechanical systems and electric circuits alike.
A boundary condition sets a constraint on a differential equation, and limits the range of its possibilities by assigning some values, by fiat.
Another way to look at it: If science is an infinite field, and "scientific progress/observation/experimentation" is a dog that is allowed to run freely through the field, then religion is the leash on the dog, and the post that is planted, which causes the dog to only be able to run around within the radius of the leash. Even if the leash can stretch, it's slow-going at the boundaries of the circle, with LOTS of resistance that holds back progress.
I think that's the sort of thing Turing was thinking about. That is, that religion is a boundary that's trying to keep back the progress of science, and keep it localized within a bubble. And I think he's right. 
Edit to add: CORRECTION - tries IN VAIN to hold it back
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