In machine learning, the sums of each node are weighted, and the sum is passed through a non-linear function known as an activation function or transfer function.
In machine learning, the activation function is used more frequently, while I think "transfer function" is more commonly used in signal processing. So anyone using them as two different terms will have to be clearer.
transfer_function = activation function + output function
A value (signal strength) to verify if the neuron will be activated and then compute an output from it. So the whole process can transfer a signal from one layer to another.
Hope this answer helps you! Study Neural Network Tutorial for more insights on this topic. Machine Learning Online Course would be a relevant subject if one wants to master the course.