I don't know if this explanation is a good one, but I'll try using Haskell syntax. In Haskell, you can have product types like:

  data CartesianCoordinate = Coord Float Float

where an element of this type is expressed as `Coord x y` where x and y are both floats. Examples of elements of this type are `Coord 1.1 0.9` or `Coord -2.9 10.0`, etc. Product types are equivalent to structs in C, if you're familiar with C.

But you can also have sum types. Instead of starting with the general idea, I'll point out that C enums are a special case of sum types:

  data Day = Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday

and then point out linked lists are more representative of the general idea:

  data ListOfFloats = Node Float ListOfFloats | End

where an element of `ListOfFloats` is for instance `Node 1.0 (Node 2.0 End)`, or `Node 0.3 End`, or just `End`.

The pipe symbol | is what makes a sum type a sum type. It means that an element of the type is either one possibility or another possibility or another possibility.

One final example is a type consisting of all possible mathematical expressions. This is also a sum type:

  data Expr = Add Expr Expr | Times Expr Expr | Negate Expr | Inverse Expr | Const Float

An element of this type can be something like `Add (Const 1.5) (Times (Const 0.2) (Const 2.8))`, which is supposed to represent the expression "1.5 + 0.2*0.8". Interestingly, you can't easily express this type in most OOP languages.

In simple set theory parlance, product types refer to Cartesian products, and sum types are set-theoretic unions.

The relevance to relational databases is that each row of a table corresponds to an element of some product type. Each row of the same table has the same product type. But there is no means defining a "table" whose elements belong to a sum type as opposed to a product type. Why is that?