Bi-elliptic transfer is a way of getting a spacecraft from one point in space to another. It takes a little longer than some other ways of traveling through space, but it uses less fuel and is safer.
Think of it like driving a car. It takes you a while to get where you want to go, but you're sacrificing time for fuel. Instead of driving straight to your destination, you take two different routes.
The first route is a big loop that is farther away from your destination. You travel around this loop so that you get some extra energy or 'speed' for the second route.
The second route is a smaller loop that is closer to your destination. You zoom around this loop with the extra 'speed' you got from the first route, so you get to your destination faster.
Bi-elliptic transfers work similarly. The first route gives extra speed and the second route takes you to your destination faster. It's a safe way to travel because you don't need to use as much fuel to get where you want to go.