A melee weapon refers to an item that can be used to perform an attack roll while in melee. These are typically superior to unarmed strikes, although exceptions (e.g. monks) exist.
When a spell affects a melee weapon (e.g. bless weapon), "melee weapon" refers to items from a specific list created by BioWare. This list consists of all standard melee weapons except lances (as lances were added in the last patch and adding them to the list was overlooked).
To be precise, the list is
bastard sword,
battleaxe,
club,
dagger,
dire mace,
double axe,
dwarven waraxe,
greataxe,
greatsword,
halberd,
handaxe,
heavy flail,
kama,
katana,
kukri,
light flail,
light hammer,
longsword,
mace,
magic staff,
morningstar,
rapier,
quarterstaff,
scimitar,
scythe,
shortsword,
sickle,
spear,
trident,
two-bladed sword,
warhammer, and
whip.
Additional melee weapons can be added with custom content, but they will not be recognized as melee weapons by spells unless the spell scripts are updated. (The list is implemented in two places — GetMeleeWeapon() in x2_i0_spells and IPGetIsMeleeWeapon() in x2_inc_itemprop. Whichever list is used by the spell in question would need to be updated, then the spell script recompiled.)