Visa-free regime between Ukraine and countries which are members of EU means that ukrainians can travel without getting visa. The same terms are inforce for EU citizens regarding thier travelling to Ukraine starting from 2005. Now ukrainians can travel freely and less expensive.
Biometric passport is enough for travelling. All the passports issued from November 2016 are biometric.
Why do we need visa-free regime? Visa-free regime let ukrainians stay in Europe for not more than 90 days. Ukranians can visit any sport and cultural events, short-term education, medical tours etc. At the same time visa-free regime does not grant Ukrainians the right to work on the territory of the EU or right for permanent residence. If you want to work on the territpry of EU and live there, you should receive special visa or resident card.