The cross mentioned is not really a cross, essential a cross-looking symbol. It is more precisely, or more generally, called the dagger symbol (\dagger in LaTeX).
It appears as a variant of the obelus (same root as a pointy obelisk), a symbol apparently invented and used by Greek scholars (potentially by Zenodotus or Aristarchus), with many sword-shaped variations:

It was used to mark corrupted, doubtful, interpolated or spurious texts, or even superfluous passages in ancient manuscripts (initially, Homeric epics). Other variants are depicted below, from Characters from the Margins of Ancient Texts:

Asterisks and Obeli: Categories of Usage provides many examples and details, such as in the following picture:

It is composed of an horizontal bar, accompanied by two dots, one above and one below. Its uses and interpretations have varied along time. For instance, the sign has been occasionally used as a subtraction sign in mathematics. It was first used for division by mathematician Johann Rahn in 1659.
It is called dagger or obelisk equally in Henry Beadnell, A guide to typography: In two parts, literary and practical, 1859.
The word obelos (ὀβελός) in Greek stands for "spit roast" or "roasting jack". It was meant to roast meat devoted to Gods. Obelisk is its diminutive form (small "obelos"). It may originate from belos (βελός), the Greek for arrow, dart, missile.
There is thus a strange weaponry connection (between the dagger and the arrow) behind this typographic sign.
\dag
) looks like a cross, which is probably why it is also used for death. It is just a glyph, used for various things. Other than footnotes, it also appears in mathematical equations from time to time, for instance to denote some type of pseudo-inverse or Hermitian adjoint. However, I can't answer the question why the shape of a dagger specifically is used as a glyph. Note that there is also a double dagger (\ddag
). More information: en.wikipedia.org/wiki/Dagger_(typography).