Dnes je příjemný den.

Because příjemný has to agree with den.

• den = a masculine singular noun
• In this sentence, den is in the nominative case because it is the subject/complement in je příjemný den
• So the adjective also takes the masculine singular nominative ending: příjemný

If the noun changed, the adjective would change too:

• příjemný den = a pleasant day
• příjemná noc = a pleasant night
• příjemné ráno = a pleasant morning

Je is the 3rd person singular form of být = to be.

So:

• je = is

The sentence literally follows the pattern:

• Dnes = today
• je = is
• příjemný den = a pleasant day

So the full structure is basically Today is a pleasant day.

Unlike in some languages, Czech normally keeps the present-tense form of to be in sentences like this.

Czech does not have articles.

That means Czech usually does not use separate words for:

• a / an
• the

So příjemný den can mean:

• a pleasant day
• the pleasant day

Which one is meant depends on context. In this sentence, English naturally translates it as a pleasant day or just Today is pleasant / Today is a pleasant day, depending on style.

Yes, Czech word order is flexible, but not all versions sound equally natural.

Dnes je příjemný den. is a very natural neutral sentence.

Why this order works:

• Dnes sets the time first: Today
• je is the verb
• příjemný den gives the description

Other word orders are possible, but they may change emphasis:

• Je dnes příjemný den. = more like Is today a pleasant day? if spoken as a question, or it can sound more marked
• Příjemný den je dnes. = unusual, strong emphasis on today
• Dnes je den příjemný. = grammatical, but not the most natural everyday phrasing

So for a learner, Dnes je příjemný den. is the best standard version.

Yes, they are related historically.

• den = day
• dnes = today

But in modern Czech, you should learn dnes as a separate word meaning today, not as a form of den.

So:

• den is a noun
• dnes is an adverb of time

You cannot use dnes as if it were just another case form of den.

A rough learner-friendly guide:

• Dnes ≈ dness
• je ≈ yeh
• příjemný ≈ roughly przhee-yehm-nee
• den ≈ den with a short e, not like English dean

A few important points:

• j in Czech is pronounced like English y in yes
• í is a long vowel
• ý is also a long vowel
• The hardest part is ř in příjemný, because ř is a special Czech sound with no exact English equivalent

If you cannot say ř yet, an approximate learner version is fine at first. Many learners start with something between r and zh.

Both are possible, but they are used a bit differently.

• Dnes je příjemný den. sounds like a normal, natural statement: Today is a pleasant day.
• Den je příjemný. means The day is pleasant and focuses more directly on the day

In your sentence, příjemný den acts as a noun phrase after je, and this is a very common Czech way to say something like It is a nice day / Today is a pleasant day.

So it is not that den je příjemný is wrong. It is just a different structure and a slightly different emphasis.

Not only. Příjemný is a flexible word and can mean things like:

• pleasant
• nice
• agreeable
• enjoyable

So příjemný den could be translated in natural English as:

• a pleasant day
• a nice day
• an enjoyable day

The exact English choice depends on context and style. In weather-type contexts, English often prefers nice day. But pleasant day is a very good direct match for příjemný den.

Yes. It is grammatical and natural.

A Czech speaker might also say things like:

• Dnes je hezký den. = Today is a nice day.
• Dnes je krásný den. = Today is a beautiful day.
• Dnes je příjemně. = It is pleasant today.

Your sentence is a normal, understandable way to describe the day. It sounds slightly more descriptive than the very common Dnes je hezky, but it is absolutely natural Czech.