“Third parties” are non-banks that provide payment initiation and account information services.
A third-party service provider could be a fintech company, a telecommunications business or a wholesaler. They require your permission to access your bank account. They firstly have to set itself up as a payment initiation service provider or an account information service provider and then register with or obtain a licence from the relevant supervisory authorities.
While the former can help you with making a payment on your behalf, the latter can provide you with a better overview of your financials.