There is no particular design for the Burial Cross - the form being whatever is vogue at the time of death
A Burial Cross, Grave Cross or Rest In Peace (R.I.P.) Cross marks the place where somebody(!) is buried.
For sure, when we die, we don't smell very nice. (Many of us don't smell so nice when alive, either1.) This is nature's way of protecting the living, warning us away from possible infectious disease by making decomposing corpses unpleasant to have around. Since Adam's time, we have dug holes, deposited bodies, and covered them up.
Burial is also a mark of respect for the deceased. The grave is the last resting place of the physical person and its precise location is important to family and friends. Consequently, a stone marker is used in most cultures that bury their dead. For Christian cultures, the tradition has been to use a stone cross marker. The cross reminds the bereaved that the soul does indeed, live on into eternity.
The modern cross above (left) was cut from marble; a relatively easy process with today's modern machinery. Each arm has a Fleur de Lis and the inscription is IHS. Earlier grave markers, reflecting the limitation of machinery and perhaps scarcity of masons, were much simpler and showed just the deceased's initials (above right).
The cross is so ubiquitous in graveyards2 that it has become a symbol for death, as shown in the advertising campaign to reduce driving speed.
In fact, the Christian cross is really a symbol of life. (But it's a clever advertisement anyway.)
See also Churchyard Cross, Funeral Cross and Wreath Cross.
1 :
"Fish and guests smell after three days"; a saying attributed to Benjamin Franklin, Oscar Wilde, and several others.
"As we say in Athens, fishe and gestes in three dayes are stale."
1580 John Lyly 'Euphues & his England' II. 81
2 :
And if you fancy a challenge, see if you can offer an alternative interpretation for the symbols on this gravestone.