Inference means using the neural net, as opposed to training it.
During inference you feed an input into the NN and it passes through it in "forwards" direction (i.e. from input to output), being modified according to the "weights" that were learnt during training, to derive the output.
During training, each training sample is first fed forwards through the NN, the same way as for inference, but then the output of the model (which at the beginning of training will be random/wrong) is compared to the correct/desired output for that training sample, and a corresponding error value will then be fed backwards (from output to input) through the NN according to the "backpropagation" mechanism to update the weights.
Training is a lot more involved than inference since it involves this backpropagation step.
During inference you feed an input into the NN and it passes through it in "forwards" direction (i.e. from input to output), being modified according to the "weights" that were learnt during training, to derive the output.
During training, each training sample is first fed forwards through the NN, the same way as for inference, but then the output of the model (which at the beginning of training will be random/wrong) is compared to the correct/desired output for that training sample, and a corresponding error value will then be fed backwards (from output to input) through the NN according to the "backpropagation" mechanism to update the weights.
Training is a lot more involved than inference since it involves this backpropagation step.