Хотя ткань тонкая, складка на юбке почти не видна.

Хотя is a conjunction meaning although, though, or sometimes even though.

In this sentence, it introduces a contrast:

• Хотя ткань тонкая = Although the fabric is thin
• складка на юбке почти не видна = the fold/crease on the skirt is hardly visible

So the idea is: you might expect a thin fabric to show the fold clearly, but in fact it is still barely visible.

Because Хотя ткань тонкая is a subordinate clause introduced by хотя.

Russian normally separates this kind of clause with a comma:

• Хотя ткань тонкая, складка на юбке почти не видна.

If the although-clause comes first, the comma goes before the main clause, just as in English:

• Although the fabric is thin, the crease is hardly visible.

Because ткань тонкая means the fabric is thin, while тонкая ткань means thin fabric.

This is a very important Russian pattern:

• тонкая ткань = adjective + noun = a noun phrase, thin fabric
• ткань тонкая = noun + adjective = predicate meaning, the fabric is thin

Russian often shows the idea of X is Y without a separate word for is in the present tense. So ткань тонкая literally looks like fabric thin, but it means the fabric is thin.

In Russian, the verb to be is usually omitted in the present tense.

So:

• ткань тонкая = the fabric is thin
• складка ... не видна = the fold ... is not visible

You only normally see forms of быть in the past or future, or in special styles:

• Ткань была тонкая = The fabric was thin
• Ткань будет тонкая = The fabric will be thin

So the missing is is completely normal Russian grammar.

Because ткань is a feminine noun, and adjectives must agree with the noun in gender, number, and case.

Here:

• ткань = feminine singular nominative
• тонкая = feminine singular nominative

A useful thing to notice is that ткань ends in -ь, and nouns ending in -ь can be either masculine or feminine. You have to learn the gender word by word. Ткань happens to be feminine.

Складка can mean fold, crease, or pleat, depending on context.

In this sentence, because it is на юбке, the best English choice is usually crease or fold. It suggests a visible line or folded place in the skirt.

So:

• складка на юбке = a fold/crease in or on the skirt

The exact English word depends on the situation, but the Russian word is very natural here.

Юбке is in the prepositional case because it follows на in a location meaning.

Here на юбке means on the skirt.

The basic pattern is:

• на + prepositional = on/in a place
• юбка → на юбке

So:

• складка на юбке = a fold/crease on the skirt

In clothing contexts, на is often used naturally for something located on a garment.

Because видна agrees with складка, which is feminine singular.

This is the short-form adjective виден in the feminine singular:

• masculine: виден
• feminine: видна
• neuter: видно
• plural: видны

So:

• складка = feminine singular
• therefore видна

That is why Складка ... видна means The fold is visible.

English speakers often expect видно, because they may have learned it first as an impersonal word meaning it is visible / one can see. But here the sentence has a specific subject, складка, so agreement gives видна.

Because не видна is the normal predicate form meaning is not visible.

Compare:

• невидимая складка = an invisible fold or a fold that is invisible
  This is an adjective directly attached to the noun.
• складка не видна = the fold is not visible
  This is a full statement.

Also, with this adjective, Russian very commonly uses the short form in predicate position:

• виден / видна / видно / видны

So складка почти не видна is the natural way to say the fold is hardly visible.

Почти не means almost not, which in natural English is often hardly or barely.

So:

• почти не видна = almost not visible
• more natural English: hardly visible or barely visible

This is a very common Russian pattern:

• почти не слышно = almost impossible to hear / hardly audible
• почти не заметно = hardly noticeable

So here the sentence means the fold can be seen only very weakly.

Because Russian uses long and short adjective forms differently.

• тонкая is the normal long form, and long forms are very common for ordinary descriptions like the fabric is thin
• видна is a short form, and short forms are especially common with certain predicate meanings such as visible, ready, necessary, glad, and so on

So this combination is natural:

• ткань тонкая
• складка не видна

In fact, the long form видная would usually not mean the same thing here. It often means something more like prominent, noticeable, or even distinguished depending on context. So for simple visible, the short form видна is the right choice.

Russian has no articles like a or the.

So nouns like ткань, складка, and юбка do not need any separate word for definiteness. Russian shows whether something is definite or indefinite mostly through context.

In this sentence, English naturally uses the fabric, the fold, and the skirt, but Russian simply says:

• ткань
• складка
• юбка

That is completely normal.