Here are the orbital elements* of Comet Halley which characterized its motion through space during the times when Edmund Halley was studying the comet. The orbital elements are specific to a particular comet and a particular apparition, and may be used to calculate the position of that comet during that apparition. Notice the similarity.

    Year      Perihelion  eccentricity   inclination     Node      Perihelion
               Distance                                            longitude 
   -------    ----------  ------------   -----------   ---------   ----------
   1581 AD    0.5812 AU     0.9678        162.9 deg    53.06 deg    107.0 deg
   1607       0.5836        0.9675        162.9        53.77        107.6
   1682       0.5826        0.9680        162.3        55.57        109.2

The perihelion distance is the Sun-comet distance at closest approach. A distance of 1 AU is the average Sun-Earth distance. The eccentricity characterizes the shape of the orbit. e=1 corresponds to a parabola; 0 < e < 1 corresponds to an ellipse; e=0 corresponds to a circle. The inclination, node, and perihelion longitude specify the orientation of the orbit in space, relative to the Sun-Earth system.

One might think that the orbital elements for a particular comet would remain the same from one orbit to the next. Actually, the other planets, notably Jupiter, exert some gravitational pull on a comet. And since the positions of the planets are different for each particular orbit of the comet, the latter changes. Also, the Sun vaporizes some material from the comet as it nears the Sun, and this produces a weak rocket-like thrust. Since comets rotate as they orbit, the direction of this thrust varies. So, this vaporization push on a comet adds to the gravitational pull in order to force the comet to follow a particular path in space.