Give us more details:

What is your neighbour piling? Is it they are building a new house? Demolish old house, building new one? Or just building an extension?

The piling would be ok if it has been approved by the authorities. That you would have to call to check.

If you're worried about your house cracking, take some pictures now and if cracks appear take pictures again and immediately notify neighbour.

Yes, it must be quite big if they need to do piling.

Piling is normally used to set the foundation so that you can build a structure on top of it.

Better check with your local council if they have approval to do what they are doing.