The distance selling thresholds apply to European sales within the EU. For most countries the threshold is €35,000 with notable exceptions being German, Netherlands, and Luxembourg at €100,000. For the UK the distance selling threshold is currently £70,000.
So, if you are selling goods from Europe, i.e. shipping from the UK and the total value sold to customers in a country in a calendar year is less than the country's threshold, then no need to register. If above the threshold, you need to register there and in your own European country if you haven't already.
Note, this threshold is different to the domestic threshold which also has to be monitored.