The Lattice modifier deforms the base object according to the shape of a Lattice object.
A Lattice Modifier can quickly be added to selected objects by selecting them all, then selecting the lattice object last and pressing Ctrl-P and choosing Lattice Deform. This will both add Lattice Modifiers to the selected objects and parent them to the lattice.
The Lattice object with which to deform the base object.
A factor to control blending between original and deformed points positions.