Let’s say the settlement period is T+2, and you made a deal on the 8/10/2018. The spot date would be 10/10/2018 (assuming no holidays!), that’s when the physical exchange would happen. Now if you don’t want physical delivery, then tomorrow (9/10/18) you can use T/N (tommorow/next) swap to delay the physical delivery by one day, T/N is essentially swap between tomorrow and the next business day. You can keep rolling your position with T/N swap.
S/N (spot next) is the period from spot date to the next business day, so the delivery in the above example would be a day later (11/10/18) if you use S/N. O/N (overnight) is the period from today to next business day(tomorrow).
So in summary using T+2 conventions:
Spot: one exchange (only one leg) on T+2.
T/N: first leg of the swap on next business day, and the second leg on the following business day.
S/N: first leg of the swap on T+2, and the second leg on the following businesss day.