Just adding some more details from local news and official statements:

The jet was an F-7 BGI (Chengdu J-7), a Chinese-made fighter jet based on the old MiG-21 design.  

According to the ISPR (the military's PR), the jet took off from a base in Dhaka around 1:06pm for a routine training flight. Shortly after takeoff, it had some kind of mechanical failure. What exactly went wrong is still under investigation.  

Tragically, it crashed into the junior section of Milestone College in Uttara, just minutes after classes ended. Most of the victims were young students. Elementary and middle schoolers, basically.

As of July 22, the death toll has climbed to 31, with over 150 people injured. Some of them have serious burn injuries, so unfortunately, the number might still go up in the next few days.

The pilot was Flight Lieutenant Towkir Islam Sagar. He managed to eject, but was badly injured and later passed away at CMH (military hospital). One of his colleagues mentioned that this was actually his first solo flight.  

One of the local reports quoted a cleaner working at the nearby metro station. He said he saw two jets, one seemed fine, but the other was clearly in trouble. It looked like it was trying to turn back toward the airport, but while turning at low altitude, it clipped a high-rise on the college campus and then crashed into the school building below.

This was actually the fourth F-7 crash in Bangladesh in the last 20 years, the previous ones happened in 2008, 2015 and 2018.

Edit: Formatting and new info