Lorentz transformation is used to recalculate some characteristics of a system from one reference frame to another. The reference frame itself is a coordinate system used to specify positions of events (including time).
Usual way to select a reference frame is to say that some specific particle rests at the origin in terms of that frame. Such reference frame is said to be bound to the particle.
In quantum mechanics one can not say that some particle rests somewhere precisely but one can say that it is true at the average. In this case the reference frame bound to the particle is the frame where the average velocity and coordinates of the particle are zero.
The reference frame must always have determined coordinates and velocity. In quantum mechanics this is achieved by using average values.
The observer A in the question uses the reference frame where the average coordinates of the particle A are constant and equal to zero. The reference frame bound to B has the velocity equal to the average velocity of the particle B w.r.t. the average position of A.