The Commission's One Stop Shop portal explains the e-commerce VAT regime: a business selling to consumers across the EU can register in a single member state and declare and pay the VAT of all member states through one quarterly return, instead of maintaining registrations country by country.
For webshops the scheme is a genuine simplification with one hidden requirement: your administration must know the customer country and the applicable rate for every sale, reliably, because the OSS return is only as good as the bookkeeping behind it. Set the shop platform and the ledger up for per-country VAT from day one and the quarterly return becomes routine.