Learn Hardcore French: Ma jambe va mieux aujourd'hui, mais j'ai encore un peu mal au dos. - My leg is better today, but my back still hurts a little.

Using être (ma jambe est mieux) is not idiomatic here and will sound wrong to native speakers. For physical or health states in progress or evolution, aller is the natural verb.

Why is it ma jambe and not mon jambe?

Because jambe (leg) is a feminine noun in French:

une jambe – a leg
la jambe – the leg

The feminine singular possessive is ma, so you get:

ma jambe – my leg

You would only use mon with masculine singular nouns (or feminine nouns starting with a vowel sound, for pronunciation reasons), e.g.:

mon bras – my arm (masculine)
mon épaule – my shoulder (feminine, but begins with a vowel sound)

What is the function of mieux in va mieux?

Mieux is an adverb meaning better (the comparative of bien).

In ma jambe va mieux, it describes how the leg is doing. Literally: my leg goes better → my leg is better.

Compare:

bien – well
mieux – better

Examples:

Je vais bien. – I am well.
Je vais mieux. – I am better.

Why is it j’ai mal au dos and not je suis mal au dos?

With body pain, French uses avoir + mal à + body part, literally to have pain at/in [body part]:

J’ai mal à la tête. – I have a headache.
J’ai mal aux yeux. – My eyes hurt.
J’ai mal au dos. – My back hurts.

Using être (je suis mal au dos) is incorrect in this context. Être mal means something like to be unwell / badly off, not to have pain in [body part].

What does mal mean here, and what kind of word is it?

In j’ai mal au dos, mal is a noun meaning pain / ache.

The structure is:

avoir mal à + definite article + body part

So:

J’ai mal au dos. – I have pain in the back / My back hurts.
Elle a mal au ventre. – She has a stomachache.
Nous avons mal aux jambes. – Our legs hurt.

Mal can be an adverb in other contexts (e.g. parler mal – to speak badly), but with body parts it functions as a noun: pain.

What is au in au dos?

Au is the contraction of à + le:

à – to / at / in
le dos – the back
→ à le dos → au dos

So mal au dos literally means pain in the back.

A few similar examples:

mal au bras – arm pain
mal au cœur – nausea (literally: pain at the heart)

What is the role of encore in j’ai encore un peu mal au dos?

Here encore means still (continuing situation), not again.

J’ai encore un peu mal au dos. – My back still hurts a bit.

Compare the two common meanings of encore:

still (continued state):
- Il est encore à l’hôpital. – He is still in the hospital.
again / more:
- Tu veux encore du café ? – Do you want more coffee again?

In this sentence, context clearly gives the still meaning: the leg is better, but the back pain continues.

What does un peu add to the meaning of mal au dos?

Un peu means a little / a bit and softens the idea of pain:

J’ai mal au dos. – My back hurts.
J’ai un peu mal au dos. – My back hurts a bit / a little.

It makes the pain sound less strong or less serious. Similar softening:

Je suis un peu fatigué. – I’m a bit tired.
C’est un peu cher. – It’s a bit expensive.

Why is the order j’ai encore un peu mal au dos and not j’ai un peu encore mal au dos?

French has a preferred adverb order. For this pattern:

avoir + (encore) + (un peu) + mal + à + body part

the natural order is:

encore (still)
then un peu (a little)
then mal

So:

J’ai encore un peu mal au dos. – correct, natural
J’ai un peu encore mal au dos. – technically understandable, but unnatural and awkward.

Can you say mon dos me fait mal instead of j’ai mal au dos? Is there a difference?

Yes, you can say both, and both are idiomatic:

J’ai mal au dos. – I have back pain / my back hurts.
Mon dos me fait mal. – My back hurts (literally: my back makes me pain).

In everyday conversation, j’ai mal au dos is slightly more common and a bit more neutral.
Mon dos me fait mal can sound a touch more explicit or emphatic, but the difference is small; you can use either.

Why is aujourd’hui placed after va mieux and not at the beginning of the sentence?

Both positions are possible:

Ma jambe va mieux aujourd’hui.
Aujourd’hui, ma jambe va mieux.

Putting aujourd’hui after the verb (as in the original sentence) is very common and neutral in spoken French.

Putting aujourd’hui at the beginning gives it a bit more emphasis, like: Today (as opposed to other days), my leg is better.

So the chosen position is just the most natural, unmarked option; the meaning doesn’t change, only the emphasis.