A Neuron firing basically implies if it'll be "activated" or not i.e. if it'll be able to output something that affects further calculation. Consider the example you gave above, if WX + b is 1.745, this value is passed into an activation function which finally decides the output value of this neuron. In a simple case, assume that this activation function is a simple binary step function then the output value becomes 1.
Hope this helps :)
WX + b
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