Odcinek lędźwiowy kręgosłupa boli.

Word by word:

• odcinek = section, segment
• lędźwiowy = lumbar
• kręgosłupa = of the spine / of the backbone
• boli = hurts, aches, is painful

So the whole phrase means something like The lumbar section of the spine hurts.

Because Polish uses the genitive case to express of the spine.

• kręgosłup = spine
• odcinek kręgosłupa = section of the spine

This is a very common pattern in Polish:

• koniec filmu = the end of the film
• drzwi domu = the door of the house
• odcinek kręgosłupa = the section of the spine

So kręgosłupa is the genitive singular form of kręgosłup.

It is in the nominative singular, because it is the grammatical subject of the sentence.

The structure is:

• odcinek = head noun, nominative singular
• lędźwiowy = adjective matching it in nominative singular masculine
• kręgosłupa = genitive singular, dependent on odcinek

So literally the subject is the lumbar section of the spine, and boli agrees with that singular subject.

They usually do, but in technical, medical, and anatomical terms, Polish often puts the adjective after the noun.

So odcinek lędźwiowy sounds like a standard anatomical label: lumbar section.

This kind of post-position is common in more formal terminology. It makes the phrase sound more like a fixed term rather than an everyday description.

You may also see:

• lędźwiowy odcinek kręgosłupa

This is also understandable and correct, but odcinek lędźwiowy kręgosłupa sounds especially anatomical/medical.

Because the subject is singular.

The subject is odcinek lędźwiowy kręgosłupa, and the head of that phrase is odcinek, which is singular. So the verb must also be singular:

• boli = hurts / is hurting

If the subject were plural, you would use bolą:

• Plecy bolą. = The back hurts / My back hurts.
• Nogi bolą. = The legs hurt.

Polish often does not state possession explicitly with body parts if it is clear from context.

English often says:

• My back hurts
• My head hurts

Polish often just says:

• Boli mnie głowa.
• Bolą mnie plecy.

So in a sentence like Odcinek lędźwiowy kręgosłupa boli, Polish does not need a word for my.

If you want to make the affected person explicit, you can add mnie:

• Boli mnie odcinek lędźwiowy kręgosłupa.

That means My lumbar spine area hurts / The lumbar section of my spine hurts.

Boleć often works differently from English.

A very common Polish pattern is:

• X boli = X hurts
• X boli mnie / cię / go... = X hurts me / you / him...

Examples:

• Głowa boli. = The head hurts.
• Boli mnie głowa. = My head hurts.
• Kręgosłup boli. = The spine hurts.
• Boli mnie kręgosłup. = My spine hurts.

So in your sentence, the painful thing itself is the subject:

• odcinek lędźwiowy kręgosłupa = the thing that hurts

Yes, it is correct and natural, but it sounds medical or clinical rather than casual.

A doctor, physiotherapist, or medical text could easily use it. In everyday conversation, many speakers would more often say something like:

• Boli mnie kręgosłup w odcinku lędźwiowym.
• Boli mnie dół pleców.
• Boli mnie krzyż.

These are less technical. So the original sentence is fine, but it sounds more like medical language.

Yes, Polish word order is fairly flexible, but the focus changes.

For example:

• Odcinek lędźwiowy kręgosłupa boli.
  Neutral if you are talking about that part of the body.

• Boli odcinek lędźwiowy kręgosłupa.
  Also possible; this puts more emphasis on it hurts.

Polish word order is often used to manage focus, topic, and emphasis, not just basic grammar. The original version is a very normal and clear choice.

Sometimes, but it is not exactly the same.

• boli = hurts, aches, is causing pain now
• jest bolesny = is painful, has the quality of being painful

So:

• Odcinek lędźwiowy kręgosłupa boli.
  = The lumbar section of the spine hurts.

• Odcinek lędźwiowy kręgosłupa jest bolesny.
  = The lumbar section of the spine is painful.

The second version sounds more descriptive and clinical. For ordinary pain in progress, boli is the more natural verb.

Very simply:

• Odcinek lędźwiowy kręgosłupa nie boli.
  = The lumbar section of the spine does not hurt.

To ask a question:

• Czy odcinek lędźwiowy kręgosłupa boli?
  = Does the lumbar section of the spine hurt?

In spoken Polish, you can also ask with intonation alone:

• Odcinek lędźwiowy kręgosłupa boli?

A rough learner-friendly approximation:

• lędźwiowy ≈ lenj-VYO-vy
• kręgosłupa ≈ kren-go-SWOO-pa

A few useful notes:

• ę often sounds roughly like en/em before consonants in normal speech
• dź is a soft sound, a bit like a very soft j sound
• ł is pronounced like English w
• stress in Polish usually falls on the second-to-last syllable

So:

• lędź-WIO-wy
• krę-go-SŁU-pa

Not exactly.

• kręgosłup = the spine, the позвоночник / backbone structure
• plecy = the back, especially the back as a body area

So odcinek lędźwiowy kręgosłupa is anatomically specific: it refers to the lumbar part of the spine, not just the back in general.

That is another reason the sentence sounds more medical than everyday. In everyday speech, people often talk about plecy; in medical or anatomical language, they are more likely to say kręgosłup or odcinek lędźwiowy kręgosłupa.