Mér líður illa í dag.

Because líða in this meaning is used with the person in the dative case, not the nominative.

So Icelandic says:

• mér líður illa = I feel bad

even though word-for-word it is closer to:

• to me feels badly / to me it feels bad

Here, mér is the dative form of ég:

• ég = I
• mér = to me / me, in dative use

This is a very common pattern in Icelandic with feelings and experiences.

Líður is the present tense form of the verb líða.

In this sentence, líða means something like:

• to feel
• to be doing
• to be faring

So mér líður illa means I feel bad or I am feeling unwell.

Be aware that líða can also mean to pass when talking about time:

• Tíminn líður hratt = Time passes quickly

So the verb has more than one use.

Because the person experiencing the feeling is not in the nominative subject form. Icelandic commonly uses líða with a dative experiencer like mér.

So even though English uses I as the subject, Icelandic does not structure it that way. The verb normally stays in the 3rd person singular form:

• mér líður
• þér líður
• honum líður
• henni líður

This is one of those places where Icelandic grammar does not match English grammar directly.

Illa is an adverb, and it means badly, poorly, or in natural English here, bad / unwell.

It is not an adjective because it is describing how someone feels, that is, it modifies the verb líður.

Compare:

• illur = bad, sick, evil, harsh (adjective; masculine form)
• illa = badly / unwell (adverb)

So:

• Mér líður illa = I feel bad
• not Mér líður illur, because that would use the wrong kind of word

It can mean both, depending on context.

Mér líður illa can mean:

• I feel sick
• I feel unwell
• I feel bad
• I’m not feeling good

It may refer to:

• physical discomfort
• nausea
• general illness
• emotional distress
• just feeling off

If the speaker wants to be more specific, they would usually add more information.

They are related, but not identical.

• Mér líður illa = I feel bad / unwell
• Ég er veikur (masculine) / Ég er veik (feminine) = I am sick / ill

The first one focuses more on how you are feeling right now. The second one states more directly that you are ill.

So if you have a headache, nausea, or just feel awful today, Mér líður illa is very natural. If you want to say you are ill in a more straightforward way, Ég er veikur / veik is also common.

Í dag means today.

It is a fixed and very common expression in Icelandic:

• í dag = today
• í gær = yesterday
• á morgun = tomorrow

So the full sentence is saying that this bad feeling is true today.

Because Icelandic often uses prepositional expressions for time.

Here:

• í = in
• dag = day

But together í dag is simply the normal way to say today.

You should learn it as a set phrase rather than trying to translate it word-for-word every time.

Yes. Icelandic word order is somewhat flexible, especially when you want to emphasize time or another part of the sentence.

These are all possible:

• Mér líður illa í dag.
• Í dag líður mér illa.

The second version emphasizes today a bit more.

But for a learner, Mér líður illa í dag is a very good basic pattern to remember.

You usually add ekki:

• Mér líður ekki illa í dag. = I do not feel bad today.

So the basic structure is:

• mér líður illa = I feel bad
• mér líður ekki illa = I do not feel bad

A natural question would be:

• Líður þér illa í dag? = Do you feel bad today?

Notice the same pattern:

• þér is the dative form of þú
• the verb stays líður

This is a very useful model sentence.

A rough English-friendly guide is:

• Mér ≈ myeh-r
• líður ≈ LEE-thur or LEE-dhur
• illa ≈ IT-lah
• í dag ≈ ee DAHG

A few notes:

• í sounds like ee
• lí is like lee
• ð is the voiced th sound in this, though in actual Icelandic pronunciation it can be softer depending on position
• ll in illa has a special Icelandic pronunciation; many learners first approximate it as tl, which is good enough at the beginning

Yes. It is very useful to memorize mér líður... as a pattern.

For example:

• Mér líður vel. = I feel good / well.
• Mér líður betur. = I feel better.
• Mér líður illa. = I feel bad.
• Mér líður mjög illa. = I feel very bad.

Learning the whole pattern will help more than trying to build it from scratch every time.

Yes. Once you know the pattern, you can swap in other adverbs or expressions.

For example:

• Mér líður vel. = I feel good.
• Mér líður betur. = I feel better.
• Mér líður hræðilega. = I feel terrible.
• Mér líður bara fínt. = I feel just fine.

So the pattern is:

• mér líður + adverb/expression

That is one reason this sentence is so worth learning well.