What object from real world could be modeled by this transfer function? What could parameters b, p1 and p2 stand for?
You transfer function models the behavior of a system. That may be a mechanical system, an electric system, etc. In your case you have a second order low pass filter.
If you calculate the step response of your system, you will notice that the system cannot follow the step. It will either grow fast, with a high slope and then start to decrease its slope when approaching the step, to never ever reach it (at least not in a finite lapse).
On the other hand, the system could grow faster to the step, reach it, then have an overshoot and start descending, reach again the step but continue descending, grow again, etc. This oscillation goes mathematically forever, or at least until its amplitude is negligible.
All this will depend on the position of the system poles.
Lets consider that the system models the behavior of, lets say, an elevator trying to reach the first floor. Here the mass of the elevator, the spring coefficients, etc. all can be used to model the system, and the step (input) is the wish to reach the first floor. The actual response of the system will be the step response, which will model the actual movement of the elevator reaching the first floor.