Mata do ćwiczeń leży na podłodze.

Do ćwiczeń means for exercise / for workouts / for doing exercises.

In Polish, do + genitive often shows purpose or intended use. So:

• mata do ćwiczeń = an exercise mat
• literally: a mat for exercises

This is very common in Polish, for example:

• buty do biegania = running shoes
• szczotka do włosów = hairbrush
• kubek do kawy = coffee mug

So do here does not mean movement toward something. It means for in the sense of used for.

Because the preposition do requires the genitive case.

The dictionary form is ćwiczenie = exercise. Its plural is ćwiczenia. After do, it changes to the genitive plural:

• ćwiczenie = one exercise
• ćwiczenia = exercises
• do ćwiczeń = for exercises

So the form ćwiczeń is there because of grammar, not because the meaning changed.

In Polish, the plural do ćwiczeń sounds the most natural for a mat used for exercise in general.

So:

• mata do ćwiczeń = a mat for exercising / an exercise mat

If you said mata do ćwiczenia, it could sound more like:

• a mat for one specific exercise
• or a mat for practice of one thing

That is not impossible in some contexts, but for the general item, mata do ćwiczeń is the normal choice.

Polish often prefers a position verb where English might simply use is.

Here, leży comes from leżeć = to lie. It is used for things that are in a horizontal position or resting flat somewhere.

A mat is flat on the floor, so leży is very natural:

• Mata leży na podłodze. = The mat is lying on the floor / The mat is on the floor.

You could also say:

• Mata jest na podłodze.

That is grammatically fine, but it is less specific. Leży sounds more natural because it describes the mat’s position.

Polish often does this with objects:

• książka leży na stole = the book is lying on the table
• butelka stoi na stole = the bottle is standing on the table
• obraz wisi na ścianie = the picture is hanging on the wall

Leży is the 3rd person singular present tense form of leżeć.

So:

• leżeć = to lie
• leży = lies / is lying

It matches mata because mata is singular.

A useful point: in the present tense, Polish verbs do not show gender. So leży can be used with masculine, feminine, or neuter singular subjects:

• telefon leży = the phone is lying
• mata leży = the mat is lying
• krzesło leży = the chair is lying

Gender becomes visible more clearly in the past tense, for example:

• mata leżała = the mat was lying
• telefon leżał = the phone was lying

Here na means on, and because this is a static location (no movement), Polish uses the locative case.

• podłoga = floor
• na podłodze = on the floor

So podłodze is the locative singular form of podłoga.

A very important contrast:

• na podłodze = on the floor (location)
• na podłogę = onto the floor (movement)

For example:

• Mata leży na podłodze. = The mat is on the floor.
• Połóż matę na podłogę. = Put the mat onto the floor.

Because Polish has no articles.

So mata can mean:

• a mat
• the mat

The exact meaning depends on context.

That means Mata do ćwiczeń leży na podłodze could be understood as:

• The exercise mat is on the floor
• An exercise mat is on the floor

In normal conversation, context usually makes this clear.

Yes. Mata is the subject of the sentence, and it is in the nominative singular.

The structure is:

• Mata = subject
• do ćwiczeń = phrase describing what kind of mat it is
• leży = verb
• na podłodze = location

So the sentence is built very straightforwardly:

[subject] + [verb] + [place]

with an extra descriptive phrase attached to mata.

Yes. Polish word order is more flexible than English because case endings show grammatical relationships.

The original sentence is neutral and natural:

• Mata do ćwiczeń leży na podłodze.

But you can also say:

• Na podłodze leży mata do ćwiczeń.

This still means the same thing, but now the sentence gives a little more focus to the location.

So the difference is usually about emphasis or information structure, not basic meaning.

A rough English-friendly guide is:

• Mata ≈ MA-ta
• do ≈ do
• ćwiczeń ≈ something like CHVEE-cheń
• leży ≈ LEH-zhih
• na ≈ na
• podłodze ≈ pod-WO-dze

A few key sounds:

• ć is a soft sound, a bit like a very soft ch/tch
• ż sounds like the s in measure
• ł sounds like English w
• rz and ż are usually pronounced the same in modern Polish

So:

• leży has the zh sound
• podłodze has ł = w

Mata do ćwiczeń is a very normal and natural way to say exercise mat.

Depending on context, you might also hear:

• mata treningowa = training mat
• mata gimnastyczna = gym/exercise mat
• mata do jogi = yoga mat

So mata do ćwiczeń is not the only possible phrase, but it is clear, common, and completely natural.