Without the specific context, I cannot give a definitive answer, but it's very likely that a "differentiable architecture" refers to a neural network that represents/computes a differentiable function (so you need to use differentiable activation functions, such as the sigmoid), i.e. you can take the partial derivatives of the loss function with respect to each parameter/weight of the neural network, so you can use backpropagation to find the gradient of the loss function, consequently, you can train this neural network with gradient descent, which is a numerical/iterative optimization algorithm for finding a (local) minimum of a function.
Most architectures you will find around are differentiable. In fact, gradient descent is the most widely used algorithm for training neural networks nowadays.