There are several meanings for indulgence
including, but not limited to:

Liberal or lenient treatment.

We take Duffy the Bichon for coffee with
us if we can be seated outdoors.
Now, you might think that Duffy is
being spoiled with an iced latte. But
you'd be wrong - that's my iced latte,
not his.

However, not shown here is Duffy's treat
which is one half of a ginger cookie.
Yes, he's also being liberaly treated, or
indulged. He snaps up those pieces of
cookie faster than my camera can catch him.