Bohmians answer this question by postulating a wave that exists in addition to the particles, and this guides the electrons by exerting on them a force. If both slits are open, this "pilot wave" passes through both slits and interferes with itself (in the classical sense of "interference"). As a result, it guides the electrons along wiggly paths that cluster at the backdrop so as to produce the observed interference pattern:

According to Bohm, the reason why electrons coming from the same source or slit arrive in different places, is that they start out in slightly different directions and/or with slightly different speeds. If we had an exact knowledge of their initial positions and velocities, we could make an exact prediction of each electron's subsequent motion.

According to the so-called "uncertainty" principle of quantum mechanics, however, it is impossible to make exact predictions of a particle's motion. Hence according to Bohm's interpretation of quantum mechanics, it is impossible to obtain exact knowledge of the initial positions and velocities. They are in possession of precise values, but we can never know them precisely. To my mind, this is not different from explaining Newton's law of gravity by postulating strictly unobservable elastic strings between all material bodies, which get thinner and weaker as they get longer.

It used to be said that this is because a measurement exerts an uncontrollable influence on the value of the observable being measured. Yet this only raises another question: why do measurements exert uncontrollable influences? This may be true for all practical purposes, but the so-called uncertainty principle does not hold for all practical purposes only. Besides, not all measurements "disturb" the systems on which they are performed. The statistical element of quantum mechanics is an essential feature of the theory. Bohm's postulate of an underlying determinism, which in order to be consistent with the theory has to be a crypto-determinism, not only adds nothing to our understanding of the theory but also precludes any proper understanding of this essentially feature of the theory.

A cryptodeterministic story has it that if we knew all existing values, then we could make exact predictions, but because some values are forever hidden from us, we can't.

As a matter of fact, there is a simple and obvious reason why hidden variables are hidden: the reason why they are strictly (rather than merely for all practical purposes) unobservable is that they do not exist.

At one time Einstein insisted that theories ought to be formulated without reference to unobservable quantities. When Heisenberg later mentioned to Einstein that this maxim had guided him in his discovery of the uncertainty principle, Einstein replied something to this effect: "Even if I once said so, it is nonsense (Quatsch)." His point was that before one has a theory, one cannot know what is observable and what is not. Our situation, however, is different. We have a theory, and this tells in no uncertain terms what is observable and what is not. In order to find out what (standard, unadulterated) quantum mechanics is trying to tell us about the nature of Nature, we of course have to assume (at least provisionally) that quantum mechanics is the right theory. Our situation is therefore different, inasmuch as quantum mechanics clearly tells us what is observable and what is not. And if the fundamental theoretical framework of physics tells us that certain things cannot be observed, then the best explanation why this is so is that, like unicorns or elastic causal strings, they do not exist.

You might think that Bohm's story allows you to retain the classical fiction that each property of a physical system exists regardless of whether it is measured. As a matter of fact, it doesn't. On this theory, energy and momentum and spin and every particle property other than position are contextual, just as the values of the spin components in the experiment of Greenberger, Horne, and Zeilinger would be if they had an existence independent of measurements. There are, in fact, theorems in the literature to the effect that any cryptodeterministic construal of quantum mechanics will invariably have to treat certain observables as contextual. This means that the value of an unmeasured observable in general depends on which observables are measured at that time.