This scenario applies to urban dual carriageways and streets where there are two or more lanes.
There are no laws in New Zealand that prevent you from passing on the left (or 'undertaking') on a motorway. expressway or dual carriageway if the vehicle in the right-hand lane is going slower. Drivers who have driven in the UK might find this odd.
However, this doesn't mean that you are allowed to travel indefinitely in the right-hand lane on a motorway or expressway if you are not overtaking.
If you are overtaking on the left then be careful of the other driver's intentions. Can they see you? Are you in their blind spot. Look for indications that the driver might move lanes.
On a single carriageway (a road with one lane travelling in your direction) you can only pass on the left if the vehicle you are passing has stopped, e.g. to turn into a driveway or road on the right, or you are directed by police to do so. You must not use a cycle lane or other lane to overtake on the left.
Filtering is when motorbikes pass between vehicles that are either stationary or moving slowly. It is legal to filter on a motorbike. Motorcyclists are allowed to do so as long as they do it safely. 'Safely' is an ambiguous term but it generally means that traffic should either be completely stopped (e.g. at traffic lights), or moving slowly (certainly no more than 40kph); the lanes must be wide enough to accommodate the bike and the vehicle; the motorbike must keep a sensible speed through the traffic (e.g. no more than 20kph faster than the vehicles being passed) This does mean that vehicle drivers should be aware of motorcyclists passing them on the left if they are in the right-hand or middle lanes. Check this guide for more detailed information on lane splitting and filtering.