The continuous icon 
indicates what kind
of cels you prefer when they are copied.
It modifies the behavior of certain commands like
New Frame,
Copy Frames, or Copy Cels.
There are two possible states:
This layer is a normal layer (with discontinuous cels): new cels will be created unlinked (cels are copied).
This layer is continuous: new cels are created in a linked way.
Generally you will prefer continuous cels for background layers (with static content), and discontinuous mode in layers that have a different cel on each frame:
This option can be switched depending on the specific situation you are working on. Modifying the option doesn't change current cels, so it only affects future operations.
SEE ALSO
Linked Cels | Layers | New Frame | Copy Frames | Timeline