There are two practical reasons why so many people in Laos ride motorbikes, motorcyles, scooters, or whatever you'd like to call them. We will use the word "motorbike" for common.
The first reason is that motorbikes are cheap and affordable for the average person because the monthly salary is extremely low by foreign standards. In Laos, people can buy a new motorbike for as little as $400 US, used motorbikes are even cheaper. It is too expensive for most Lao people to own a car, given the price of the vehicle, the money spending on fuel, and the cost of maintaining it. People who own a private car usually operate some kind of business, or they work for a foreign company.
The other reason is the advantage of motorbikes. It's much more convenient to ride motorbikes in Laos because the streets are quite narrow, roads have cracks and it's easy to go around them and get to places quicker dodging between the traffic jams. Also people can drop by on their motorbike and purchase something along the streets. Motorbikes are quite small and very suitable for Lao people, it's not uncommon to see 3 or 4 people together on a motorbike.
Over 20 years ago, the streets of Vientiane were full of bicycles, now they are full of motorbikes. Even people living in countryside of Laos now use motorbikes because the living standard has improved. Motorbikes are the main cause of accidents in the cities. That is the reason why many foreign visitors feel scared when they cross the streets. It is now compulsory to wear a helmet when riding a motorbike but many riders who know the roads very well disobey the rules because they know that the police aren't around.