Jo mere tøj der ligger i kurven, jo sværere er det at finde mine sokker.

It is a very common Danish pattern used for comparisons of the type the more ..., the more ... or the more ..., the harder ....

So:

• Jo mere ..., jo sværere ... means
• The more ..., the harder ...

You can think of jo here as introducing each half of a linked comparison.

A few similar examples:

• Jo mere du læser, jo bedre bliver du.
  = The more you read, the better you get.
• Jo ældre han bliver, jo roligere bliver han.
  = The older he gets, the calmer he becomes.

So in your sentence, the two halves are:

• Jo mere tøj der ligger i kurven
• jo sværere er det at finde mine sokker

They belong together as one comparison.

Because tøj is normally treated as an uncountable / mass noun in Danish, much like clothing in English.

Use:

• mere for uncountable nouns
• flere for countable plural nouns

So:

• mere tøj = more clothing
• flere sokker = more socks

Compare:

• mere vand = more water
• mere tid = more time
• flere bøger = more books
• flere mennesker = more people

Even though English often says clothes, Danish tøj behaves grammatically more like clothing.

Grammatically, tøj is usually treated as a singular mass noun, even though it refers to many items of clothing.

That is why the sentence says:

• tøj der ligger ... not
• tøj der liggere ... or any plural-style agreement

In Danish, verbs do not change for singular and plural the way they do in some other languages, but the important point is that tøj is not used like a normal countable plural noun.

So:

• mit tøj = my clothes / my clothing
• meget tøj = a lot of clothes
• mere tøj = more clothes

You would not normally count tøj directly. If you want to count items, you would use words like:

• tre stykker tøj = three items of clothing
• mange klædningsstykker = many garments/items of clothing

Here der is a relative pronoun, meaning that / which / that is in English.

So:

• tøj der ligger i kurven means
• clothes that are lying in the basket

It introduces a relative clause that describes tøj.

Compare:

• bogen der ligger på bordet = the book that is lying on the table
• manden der taler = the man who is speaking
• maden der står i køleskabet = the food that is in the fridge

In everyday Danish, der is very commonly used in relative clauses, especially when it is the subject of the clause.

In many cases, Danish can use both der and som in relative clauses, but der is especially common when it is the subject of the relative clause.

Here, in:

• tøj der ligger i kurven

the thing doing the action of ligger is tøj, so der works very naturally.

Very roughly:

• der often appears when the relative word is the subject
• som is also possible in many relative clauses, but the choice depends on structure and style

For a learner, the safest practical takeaway is:

• noun + der + verb is a very common and natural pattern

Examples:

• bilen der holder udenfor = the car that is parked outside
• pigen der synger = the girl who is singing

So tøj der ligger i kurven is completely normal Danish.

Ligge means to lie or to be lying / located in a lying position, and in Danish it is often used for things resting somewhere.

So:

• tøjet ligger i kurven
  means something like
• the clothes are lying in the basket

Danish often uses position verbs where English might simply use is:

• Bogen ligger på bordet. = The book is on the table.
• Nøglerne ligger i tasken. = The keys are in the bag.
• Hun sidder i stolen. = She is sitting in the chair.
• Billedet hænger på væggen. = The picture is on the wall.

You could say er i kurven, but ligger i kurven sounds more natural because clothes are physically lying there.

Sværere is the comparative form of svær = difficult/hard.

The basic pattern is:

• svær = difficult
• sværere = more difficult / harder
• sværest = most difficult / hardest

In the sentence:

• jo sværere er det ... = the harder it is ...

This matches the jo ... jo ... comparison structure, which normally uses comparatives:

• mere = more
• sværere = harder
• bedre = better
• større = bigger
• mindre = smaller

So both halves of the sentence use comparative forms, just as in English: the more ..., the harder ...

Because Danish uses verb-second word order in main clauses, and the whole jo sværere part is functioning as the first element of that clause.

So the structure is:

• jo sværere = first element
• er = verb
• det = subject

That gives:

• jo sværere er det at finde mine sokker

This is very typical Danish word order. When something other than the subject comes first, the verb usually comes immediately after it.

Compare:

• I dag er jeg træt. = Today I am tired.
• Derfor kommer han ikke. = Therefore he is not coming.
• Jo større huset er, jo dyrere bliver det. = The bigger the house is, the more expensive it becomes.

So jo det er sværere would not be correct here.

This det is a formal subject or dummy subject, similar to English it in sentences like:

• It is hard to find my socks.

In Danish, this is very common:

• Det er svært at forstå. = It is difficult to understand.
• Det er dejligt at være hjemme. = It is nice to be home.
• Det er vigtigt at øve sig. = It is important to practise.

So:

• jo sværere er det at finde mine sokker literally follows the same pattern as
• it is harder to find my socks

The real content comes in the infinitive phrase:

• at finde mine sokker = to find my socks

Because Danish often uses the structure:

• det er + adjective + at + infinitive

Examples:

• Det er svært at lære dansk. = It is hard to learn Danish.
• Det er nemt at glemme det. = It is easy to forget it.
• Det er hyggeligt at være her. = It is cosy/nice to be here.

So in your sentence:

• sværere er det at finde mine sokker means
• harder it is to find my socks

The infinitive marker at is the same word you use before verbs in dictionary form:

• at finde = to find
• at læse = to read
• at sove = to sleep

Because kurven means the basket, while en kurv means a basket.

Danish often uses the definite form when the object is understood from the context. For example, if there is one laundry basket everyone knows about, then i kurven is natural.

Forms:

• en kurv = a basket
• kurven = the basket

This definite form is made by adding the article to the end of the noun.

Other examples:

• en stol → stolen
• en bog → bogen
• et hus → huset

So i kurven simply means the speaker has a specific basket in mind.

Because the speaker wants to say my socks, not just the socks.

Danish possessives work like this:

• min sok = my sock
• mine sokker = my socks

Since sokker is plural, Danish uses mine.

Compare:

• min bog = my book
• mit hus = my house
• mine bøger = my books

So:

• mine sokker = my socks
• sokkerne = the socks

Both are possible in other contexts, but they mean different things.

Sometimes yes, but they are not always exactly the same in usage.

In modern everyday Danish:

• sokker is very common for socks
• strømper can also mean socks/stockings, but often sounds broader or can suggest longer hosiery depending on context

For many learners, sokker is the safest everyday word for ordinary socks.

Examples:

• et par sokker = a pair of socks
• uld­sokker = wool socks

So the sentence sounds very natural with mine sokker.

It is natural and completely normal Danish.

The jo ... jo ... structure is common in both spoken and written language. The sentence sounds like something a native speaker could easily say in everyday life.

It has a slightly neat, well-structured feel because of the comparison pattern, but it is not stiff or unnatural.

A speaker might also say similar things like:

• Jo mere rod der er, jo sværere er det at finde noget.
• Jo længere jeg venter, jo trættere bliver jeg.

So this is definitely a useful real-life pattern to learn.