Compressor stall (induced by bird strike)
Its loud and spectacular, boooom, booom, boom-boom.
The bird probably damage and bent some stator vanes** The vanes guide air through the engine, which lowers the air's angle of attack going into each successive turbine stage or rotor blades. The engine is stalling and un-stalling.
At high power an "upset", such as a bird strike, can cause the engine to go thru a "start-unstart cycle" or surge. If the pilot pulled the thrust back, it probably would run fine at lower power, stopping the cycling. Most airlines have a minimum altitude for dealing with an engine problem. At low altitudes (aka right after takeoff) all they can or trained to do is hang on, keep the power on, get altitude, while listening to the engine do its boom-boom thing, than work the problem. Its not comfortable, but its not as bad as it sounded or looked, but it does look and sound spectacular.
** A Jet engine is really a bunch of wings flying around in circles, and these blades can stall just like any wing. Stators guide air to prevent blade stalls. Some are fixed and some move. When you get a stall the engine will surge. At worst a stall will progress into what you see in this video. The audio did not do it justice, because it sounds like a cannon. It's pretty rare.
The engine was in little danger of coming apart, catching on fire or blowing up. Even if the bird did more damage or a blade let lose, it would (should) be contained in the fan shroud. Often the fan shroud is made of thick metal or in bigger engines sometimes Kevlar. Kevlar fabric is wrapped around the fan housing but with out resin; It's like a soft bullet proof vest but with many more layers. I have had few bird strikes, one I sucked into and through the engine for sure. You don't always know with a big engine and small bird; the engine does not even hick-up. You may see blood on the cowl or shroud or wing leading/tail edges. Often you don't see or hear them hit in flight. I got one in the nose gear and it was still there during walk around, kind of; it was a mess. Poor thing.
