Trajectory is one of important concepts of the Classical mechanics that assumes that at each moment of time each particle has some definite coordinate. Often i it assumed that the space is 3-dimensional, so, the coordinate can be expressed as set of 3 real numbers.
Coordinate of each body as function of time are called trajectory.
Also the term trajectory may refer to the set of coordinates that the body passed during its movement, without to specify the moment of time when the bogy reaches the specific coordinate.
In quantum mechanics, term trajectory may refer to the set of states, the wavefunction of a system passes during its evolution in the Schroedinger representation. For certain states quasi-classical states, the results of the quantum consideration can be interpreted in terms of the classical trajectory. The transition from quantum consideration to classical implies the loss of information; so, the classical interpretation implies the probability.