Bohm came up with his own version of
quantum mechanics which (it has now been proven) makes exactly the same predictions as the standard QM formalism, but has a "realistic" interpretation, involving point particles with real paths.
In the two slit experiment, a series of particles are shot, one at a time, towards a detector, with a double-slitted wall interposed.
Notoriously, even if the particles arrive one at a time, the detector shows the distribution of the particles has interference fringes as though the particle had propagated like a wave, going through both slits. Controversy still rages about the significance of this result.
In Bohm's model, there is a moving point particle, accompanied by a "pilot wave", which influences the path taken by the particle. The particle surfs along in particular spots on the wave:
_ _
' ` ' `
~.^ / \ @ / \ ^.~
V \ / V
`_'
When the pilot wave passes through the two slits, and interferes with itself, Bohm showed, it produces a set of possible paths behind the slits which result in the fringed distribution seen in the experiment.
Technically, the Schroedinger equation is used to produce a wave function (the "pilot wave") which then generates a velocity field, determining the motion of the particles. The point particles are taken to have real positions and momenta. The nonlocal twist comes in since the wave function takes place not in "physical" 3-dimensional space, but in a higher dimensional "configuration space" depending on the (simultaneous!) position of all particles in the environment.
This aside, perhaps Bohm's most notable contribution to the science was in formulating a thought experiment - a variant of the Einstein-Podolsky-Rosen paradox, using spin rather than position and momentum - which proved to be experimentally testable, and showed conclusively that the Bell inequalities were violated by straightforward quantum theory, leading to the widespread acceptance of nonlocality in the 1960's. (This work was published in Quantum Theory (1951) and Physical Review 85, pp. 169-193.)
Suspicions about Bohm's political allegiances on the part of the authorities were responsible for his being ejected from the Manhattan Project.
Information from the Introduction to Bohmian Mechanics at:
http://www.mathematik.uni-muenchen.de/~bohmmech/Poster/post/postE.html