So hopefully you understand what the $\sum$ symbol means, it's just a summation across all of those indices. In this case we have our weight vectors
and our vector $y$. The neuron then is going to compute the new value of y_i, based on a dot product of w_i with y. Hence
is just dot product of w_i and y, where both are n-dimensional vectors.
Then f is an activation function, it could be a preceptron or it could be a linear node. So it may output the value of the net, or it may output a 0 or a 1 based on the value of the summation. Or it could have some non-linear neuron it all depends on the network.