To invert a chord is to change the order of the chord's notes. In an inverted chord, the root is NOT the lowest note.
Major Triad Construction = 1 3 5
First Inversion = 3 5 1
Second Inversion = 5 1 3
Perhaps the quickest way to understand the concept is to study the staff in the examples below. The way the notes stack on the staff shows how they change the order in each inversion.