Jo blødere stoffet er, jo mere vil barnet have skjorten på sig.

It is the Danish way to express the ... the ... comparisons in English.

So:

• Jo blødere stoffet er = The softer the fabric is
• jo mere vil barnet have skjorten på sig = the more the child will want to have the shirt on

This pattern shows that one thing changes together with another:

• Jo mere du læser, jo bedre bliver du.
  The more you read, the better you get.

Blødere is the comparative form of blød = soft.

So the forms are:

• blød = soft
• blødere = softer
• blødest = softest

In this sentence, Danish needs the comparative because the jo ... jo ... structure compares degrees:

• jo blødere = the softer