Dziś wiatr jest mocniejszy niż wczoraj.

They both mean today.

• dziś is a shorter form
• dzisiaj is the full form

In everyday Polish, both are very common and natural. Dziś can sound a little more concise or slightly more written/stylistic in some contexts, but in this sentence either works:

• Dziś wiatr jest mocniejszy niż wczoraj.
• Dzisiaj wiatr jest mocniejszy niż wczoraj.

Both are correct.

In the present tense, Polish normally does use the verb być (to be) in sentences like this.

So:

• wiatr jest mocniejszy = the wind is stronger

You usually cannot omit jest here in normal standard Polish.
Without it, Wiatr mocniejszy niż wczoraj sounds incomplete as a full neutral sentence.

So unlike some languages where is can be dropped, Polish needs jest in this kind of statement.

Because the sentence is making a comparison.

• mocny = strong
• mocniejszy = stronger

The word niż (than) signals comparison, so the adjective must be in the comparative form:

• mocny wiatr = strong wind
• wiatr jest mocniejszy = the wind is stronger

It is the comparative form of mocny.

• mocny = strong
• mocniejszy = stronger

This is not formed in the same simple way as English strong → stronger. In Polish, adjective comparatives are often formed by changing the stem and adding endings like -szy or -ejszy / -niejszy.

So this is something you should mostly learn as a vocabulary pattern:

• mocny → mocniejszy

It is a very common and useful pattern, even if it does not look completely transparent at first.

Because it has to agree with wiatr.

In Polish, adjectives match the noun in:

• gender
• number
• case

wiatr is:

• singular
• masculine

So the adjective also takes a masculine singular form:

• wiatr jest mocniejszy

If the noun changed, the adjective form would change too. For example:

• burza jest mocniejsza = the storm is stronger
  because burza is feminine

Niż means than in comparisons.

So:

• mocniejszy niż wczoraj = stronger than yesterday

It is the normal word to use when comparing one thing or situation with another.

Usually, not in this sentence.

In Polish comparisons, both niż and od can sometimes correspond to English than, but they are not interchangeable in every structure.

Here, wczoraj is an adverb meaning yesterday, so niż wczoraj is the natural choice:

• Dziś wiatr jest mocniejszy niż wczoraj.

If you said od wczoraj, it would usually mean since yesterday, not than yesterday. So that would change the meaning.

Wczoraj is an adverb, not a noun here, so it does not change for case.

That is why it stays simply:

• niż wczoraj

A learner might expect some case ending after niż, but here there is none, because wczoraj is an indeclinable time adverb.

Because Polish has no articles.

English distinguishes:

• a wind
• the wind

Polish does not use words like a or the, so wiatr can mean:

• wind
• the wind

The exact meaning depends on context. In this sentence, English naturally translates it as the wind.

Yes. Polish word order is more flexible than English word order.

The given sentence is completely natural:

• Dziś wiatr jest mocniejszy niż wczoraj.

But you could also say:

• Wiatr jest dziś mocniejszy niż wczoraj.

Both mean essentially the same thing. The difference is mostly about emphasis and style.

• starting with Dziś emphasizes today
• starting with Wiatr emphasizes the wind

Both can work.

• mocniejszy = stronger
• silniejszy = stronger / more powerful

With wind, Polish speakers often use silny / silniejszy as a very common choice, but mocny / mocniejszy is also correct and natural.

So this sentence is fine. A very similar alternative would be:

• Dziś wiatr jest silniejszy niż wczoraj.

A rough guide is jish, but that is only approximate.

More specifically:

• dz here sounds like a soft sound similar to the beginning of jeep, but softer
• i softens the consonant
• ś is a soft sh sound

So dziś is short and ends with a soft hushing sound.

If you already know Polish spelling a little:

• ś is always a soft consonant
• dzi represents a soft sound, not three fully separate English-style sounds

It can, but Polish does not have to match English word order.

English often prefers:

• The wind is stronger today than yesterday

Polish often puts time expressions early:

• Dziś wiatr jest mocniejszy niż wczoraj.

This is very normal. Polish frequently places words like dziś, wczoraj, jutro, teraz near the beginning of the sentence, especially when setting the time frame first.

In practice, it means the wind in the current situation.

Because Polish has no articles, wiatr does not explicitly say a wind or the wind. But in a sentence like this, it is understood as the wind outside / the wind we are experiencing now.

So even without an article, the meaning is naturally specific from context.