The demand horizon (field FOH on product-site) defines when a forecast is defined as expired by MRP / MPS processing (when setup HORDEM on the MRP /MPS requirement parameter is on). The whole benefit is to define how the system identifies a forecast that is obviously incorrect. 

For instance, should you replenish your stock (purchased, manufactured or subcontracted product) if you have a forecast for tomorrow but no sales order? By setting your demand horizon (and combined with HORDEM = ticked) to 1 week, you will ensure that MRP will consider for the next week only sales document (SOF and SOP) but not forecasts (SOS). 

Another example is a forecast that is below the actual sales: in 2 weeks time (after he demand forecast) you have 100 as forecast (SOS) but an actual sales of 150 (SOF). MRP / MPS will consider that the actual need to fulfilled is MAX (SOS; SOP+SOF) so 150 in this case. 

I hope this is clearer now.

So if my demand horizon is set to 0, it'll always consider the greater of the two, either the forecast or the demand ?

What about when the sales order is shipped.  How does the demand horizon affect the MRP results ? 

I know I am 3 months late on this topic.. LOL. But Yes. if you set the demand horizon to 0, it will always consider the greater of the two. A couple things to keep in mind.

1. This only works if the "Forecast offset" checkbox is checked on the "Setup->stock->requirement parameter" 

2. When the system offsets the real demand against the forecast, it's comparing the total demand within each bucket. Since the smallest forecast time period is by week, you want to make sure the bucket size is by week outside of your demand horizon. 

A shipped order is not consider as demand. 

If the order was within the demand horizon, MRP will not ask you to fulfill the order because it's consider fulfilled.

If the order was outside of the demand horizon, and for some reason you shipped early, MRP will not see that as a firm demand, and will offset between the forecast and remaining open orders.