To figure the amount of phase angle change in oscillator i due to coupling with other oscillators, for each other oscillator j, take the difference of the phase angles of i and j and add some function (the coupling function) of this difference to the sum.
This equation expresses the change in phase angle of oscillator i due to coupling with other oscillators in terms of the difference in phase angles of those oscillators and oscillator i. Obviously this distance matters, but precisely how it matters, we will leave unspecified at the moment and simply say that there is some function f of the difference which determines the change in phase angle. The large sigma means that we are summing the effects of the phase angles differences over all of the oscillators. We refer to each oscillator with subscript j (to distinguish it from oscillator i, the one we are concerned with at the moment), and j has every value from 1 up to N, the total number of oscillators. The sigma says that we are to add the quantity after the sigma for all of these values of j. It is just a shorthand notation for a number of additions, used here because we do not in general know how many additions we will need to write down (because N can take on different values). Finally the whole sum is multiplied by a constant (C) so that we can control how fast coupling takes place. If C is close to 1, then on each time slice each oscillator moves quickly in the direction of other oscillator. If C is small, say, .01, each oscillator moves only very slowly in the direction of the others. Note that we still aren't done because we haven't yet said what the coupling function f actually is.
It will be convenient to think of phase angle differences as varying from -.5 to +.5. A difference of 0 means that the oscillators' phase angles are equal; they are perfectly aligned. A negative phase angle difference means that the oscillator we are considering, oscillator i, is behind the other oscillator, oscillator j. In general, coupling should cause oscillator's i's phase angle to increase in this situation, so the value of the coupling function will be positive. A positive phase angle difference means that oscillator i is ahead of oscillator j. In this case, coupling should in general cause oscillator i's phase angle to decrease, so the coupling function should have a negative value. Note that a difference of -.5 is the same as a difference of +.5; at that point we cannot say whether the I is ahead of or behind j.