An Annulet Cross is simply a posh heraldic word for a cross with circular adornments stuck on the end of the cross arm(s).
Annulet means a small ring, or more accurately, the vacant space within the ring.
Nullus is Latin for 'not any' or 'none', and an Annulet is a ring – its usefulness being the fact that it is hollow; i.e. not a disc.
In architecture, an annulet is the torus or flat decorative moulding that encircles a column, typically at the base and/or just beneath the capital. They were used as extensively by the Greeks in their Doric, Ionic and Corinthian columns.
(A doughnut is a sort of annulet; sweet, but not as durable as the stone annulets used by the Greeks.)
In heraldic terms, an annulet is any charge in the shape of a hollow roundel. We can see this in the Celtic Cross and the Sun Cross. The term could also be applied to crosses such as the Wedding Ring Cross or any cross which includes circles or rings. In heraldry, if Annulet Cross limbs do not reach the edges of an escutcheon (shield), it is called an Annuletty Cross.
For the image shown above, small Votive Crosses like these have been found hanging in Byzantine churches in Greece. The annulets in these crosses have no particular meaning; simply they are screw holes by which the cross is attached to a board.