An onward ticket is a booking of any flight/train/bus originating from the country about to be entered into another country. For example, a traveller is planning to go for a multi-city travels in South East Asia. So this person booked a plane ticket from Phuket to Singapore and then another bus ticket from Singapore to Malaysia. In this scenario, the bus ticket to Malaysia is the onward ticket.
On the other hand, round trip ticket is a confirmed booking of any flight/train/bus from the country about to be entered back to the country of origin. Basing from the example above, a round trip ticket would be like Phuket-Singapore-Phuket.
Having a onward ticket or a confirmed round trip ticket is very crucial upon entering a new country. So if you have an open itinerary and plan to travel to multiple countries, then booking an onward ticket is your best solution to your problems. This is especially useful when a country you are traveling to require a visa or proof of travelling upon entering.