What are "folded" and "pivoted" tables?
It's just a different way of representing the data. Also known as wide (pivoted) and long (folded). As an example and to keep it simple, imagine that we have a record with 3 properties: id, name, description in the wide (pivoted) version each property would be its own column like so:

CREATE TABLE `example_table` (
  id int not null,
  name archer(50) not null,
  description archer(100) null
)


In the long (folded) format you would have two columns like so:

CREATE TABLE `example_table` (
  property varchar(50) not null,
  value varchar(100) not null
)


The later gives you greater flexibility if the columns are not known in advance or are likely to change often. However, it is generally more complicated to implement because you have to design a way of knowing what type the value is, and then you have the overhead of serialization/deserialization to the storage type (in this example varchar(100)).

The wide format is better when the properties do not change very often and are known in advance. This will offer better performance but will be less flexible if changes are required.

Generally, where possible choose the wide format when you know the structure of the data you are storing, and choose long if you need maximum flexibility and are willing to accept the added complexity.