What does S1S4 (or similar) mean in the context of cherries?

Question

I read about cherries, and each cultivar is associated to a mark like S₁S₄, S₃S₆ - or similar.

I understand this is something related to genes, but could not find a comprehensive explanation on this topic.

I though do find explanations like this:

The fertility in sweet cherry is determined by a gametophytic self-incompatibility system, controlled by a multi-allelic S-locus who prevents self-pollination.

However, I have the hardest time figuring out the meaning of such sentences. :(

What do those marks mean? What is the practical value of that information to gardeners? How do I explain them to my neighbor? (I certainly would not like to tell him: "Your cherry's multi-allelic S-locus controls its gametophytic system".)

Answer 1

S1S4, S3S6 and others are Pollen Groups for Cherries. Only some species of Cherry tree are capable of pollinating themselves (such trees are referred to as self-fruiting, or self-pollinating). However many are not, and because Cherry trees are produced by grafting, other trees of the same variety are, genetically speaking, the same plant. If 2 Cherry trees have the same S-types they are not a compatible breeding pair and will need an alternate pollen source to make fruit. So if you are looking for cherries you either need a tree that is Self-Fruiting, or at least 2 trees in different pollen groups.

Source: https://anfic.com.au/wp-content/uploads/2020/07/ANFIC-Sweet-Cherry-Pollination-Table-06072020.pdf Pollen Group Chart