It becomes much easier to understand if you think in terms of probability. In reality, there will be chances of electrons being anywhere on the detector, it's just that the probability of them ending up in those 'bands' is higher. This is the same as a reflection of a beam of light on a surface like a mirror: sure, you can draw the normal and then state the law of reflection that incoming angle and reflecting angle are the same. In reality however, photons can end up anywhere - it's just that the probability of them ending up at the place where the law states they will is highest. In particle physics, these are determined by wave functions.
If you fire single particles, such electrons, through two slits 1 and 2, the wave functions ϕ1 and ϕ2 along each path describe the probability that they will pass through the slits, with the total wave function at the detector being ϕdet = ϕ1 + ϕ2. The probability of detecting a particle is then ϕdet² = ϕ1² + ϕ2² + 2|ϕ1||ϕ2| cos Δξ, where |ϕ1| and |ϕ2| are the amplitudes of the waves and Δξ is their phase difference at the detector. The result is a series of bright and dark bands depending on whether the two wave fronts are in phase (cos Δξ = 1) or out of phase (cos Δξ = –1), meaning either a high or low chance of detecting a particle. But if you close, say, slit 2, then ϕ2 = 0 you see a distribution of particles due solely to slit 1 (ϕdet² = ϕ1²). If you close slit 1, then ϕ1 = 0 and the distribution is given by (ϕdet² = ϕ2²). You can work out the interference term by measuring the signals from both slits individually, and by then measuring the yield with both slits open.
In other words, the two slits just change the probability of where particles are detected and result in an interference pattern. There is no magical need for one particle to know there is a second slit.
Edit: this video (at the current time stamp) should help with some of this understanding: