The difference pertains to the rules used to redraw and possibly reposition
the object when the graph (and especially its scales) changes: Should
it stay "fixed" where it was originally in the relation to the
graph window (e.g., perfectly in the middle) but lose its relation to
the specific plots, which are now drawn in a different place (fixed),
or should it rather follow the plots as the scales or plot positions change
(dynamic).
Specifically:
Dynamic mode. In the dynamic mode, all custom objects placed anywhere on the graph (e.g., drawings, arrows, text, embedded or linked graphs, or other artwork) will be anchored against the current X- and Y-axis scale coordinates. Thus, they will be dynamically attached to specific "logical" graph locations (and not absolute positions within the graph window). When the graph is rescaled or moved within its window, the relations between the custom (dynamic) objects and the respective graph components will not change (e.g., an arrow will still mark the same point on a line graph even when the graph is rescaled and this point is now in a different place in the window).
Fixed mode. In the fixed mode, however, all custom objects will always remain in their absolute positions, anchored only against the proportions of the window. For example, if you add a footnote at the bottom of the graph, it will always remain on the bottom even if the graph is rescaled.
The status of objects can be adjusted in the respective Object Properties dialogs. Note that some objects may have two anchor points, and then each can have a different status. For example, the head of the arrow can be dynamically related to a detail in the plot, but its tail can be fixed at the very bottom of the graph window where the label or comment is located.