gwlee: It all comes down to simple physical chemistry.
The titanium used for structural components in buildings/aircraft/space shuttles/knives has a molecular structure called a body centered cube. Steel, heated to austenitec ranges and higher, has a face centered cube. Basically, the ways in which the atoms are bonded to each other have distinct types; and even individual elements can form different types of structures based on their bonds. For example, carbon can be formed in the soft graphite - which is essentially a hexagonal lattice of carbon bonds - or it can form the extremely hard and dense diamond, which is a tetrahedral face centered cube. These are called allotropes.
As there are only a set number of atoms within a given volume, each allotrope of an individual element (if it has more than one) will be of a different density: simply, if you pack more atoms in a given volume, it will have a greater volume.
In application to this question of Titanium being lighter, Titanium has two advantages. Titanium has a 47.867 Standard Atomic Weight, in comparison to Iron's 55.845 - Titanium, being higher on the periodic table, has less mass at the atomic level. Secondly, for our purposes, stainless steels used for knives is at least in the austenitec phase or higher. Structural Titanium's allotrope is that of a body-centered cube, where austenitec or higher Iron allotropes are face-centered cubes. Quite simply, in a body-centered cube there are 9 atoms which bond in the given volume, where in a face-centered cube there are 14. Thus, Titanium and Iron, in the uses in which we are discussing - that of knife components - will always be lighter because it is:
A. Lighter at the atomic level.
B. Less dense at the molecular level.
To get a more in depth explanation, the wikipedia article on Bravais Lattice's would be a good start.
http://en.wikipedia.org/wiki/Bravais_lattice