Learn Hardcore Icelandic: Íþróttir hafa góð áhrif á heilsuna hennar, svo hún reynir að fá hreyfingu daglega. - Sports have a good effect on her health, so she tries to get exercise daily.

Íþrótt (singular) exists but is much less common and more specific, like “a particular sport”.
Using the plural for a general category is very natural:
- Íslendingar elska íþróttir. – Icelanders love sports.

So Íþróttir hafa góð áhrif… is best understood as “Sports have a good effect…”, even though English might also say “Sport has a good effect…” or “Exercise is good…”.

What does hafa góð áhrif á literally mean, and how is this expression used?

Literally, hafa góð áhrif á means “to have good effects on” or “to have a good influence on”.

hafa áhrif á e-ð = to affect something / to have an effect on something
Adding góð makes it positive: have good effects on…

Some examples:

Kaffi hefur lítil áhrif á mig. – Coffee has little effect on me.
Svefn hefur mikil áhrif á heilsuna. – Sleep has a big effect on health.

In your sentence, Íþróttir hafa góð áhrif á heilsuna hennar = “Sports have a good effect on her health.”

Why is it góð áhrif, not góðar áhrif or góður áhrif?

Because áhrif is neuter plural, and the adjective must agree with it in gender and number.

Noun: áhrif – neuter plural (it’s almost always used in the plural and looks the same in nom./acc.).
Adjective góður (good) in different forms:
- masc. sg. nom.: góður
- fem. sg. nom.: góð
- neut. sg. nom./acc.: gott
- neut. pl. nom./acc.: góð

So:

góð áhrif = correct (neuter plural)
góðar áhrif = wrong (that’s feminine plural)
góður áhrif = wrong (that’s masculine singular)

What does á heilsuna hennar literally mean, and what case is heilsuna in?

Literally, á heilsuna hennar is “on her health”.

heilsu is the accusative singular of heilsa (health), a feminine noun.
The ending -na is the definite article, so:
- heilsa – (a) health
- heilsu – health (accusative, no article)
- heilsuna – the health (accusative definite)

Here, á + accusative with áhrif á means “to affect / have an effect on”. So:

á heilsuna hennar = “on her health” (with “health” definite: the health).

Why is it heilsuna hennar and not hennar heilsu?

Both orders are grammatically possible, but they’re not used the same way.

Noun + definite article + possessive after it
- heilsuna hennar = “her health” (neutral, normal way to say it)
- Pattern: húsið mitt – my house, bókin hans – his book
Possessive before the noun
- hennar heilsa / hennar heilsu = “her health”, but sounds more emphatic or contrastive, like “HER health (as opposed to someone else’s).”

In everyday, neutral style, heilsuna hennar is the natural choice here.

Could you use sína instead of hennar here, as in á heilsuna sína?

No. Sína is a reflexive possessive pronoun. It is only used when the possessor is the subject of the same clause.

Hún hugsaði um heilsuna sína. – She thought about her own health.
- Subject = hún
- Possessor = hún → use sína

In your sentence:

Subject of the first clause is Íþróttir (sports), not the woman.
heilsuna hennar refers to her health, not the health of the sports.

So heilsuna sinna would mean “their own health” (the health of the sports), which is nonsense.
Therefore heilsuna hennar is correct.

What role does svo play here? Is it the same “so” as in “so much” or “so beautiful”?

Here, svo is a conjunction meaning “so / therefore”, introducing a result:

Íþróttir hafa góð áhrif á heilsuna hennar, svo hún reynir…
→ “Sports have a good effect on her health, so she tries…”

This svo links cause and effect.

There is also another svo used as an adverb of degree, like English “so (very)”:

Hún er svo þreytt. – She is so tired.
Þetta er svo gott. – This is so good.

Your sentence uses the conjunction meaning “so, therefore”, not the “so (very)” one.

What does reynir mean, and how does reyna að + infinitive work?

Reynir is the 3rd person singular present of reyna – “to try”.

Infinitive: að reyna – to try
3rd person singular present: hún reynir – she tries

The construction:

reyna að + infinitive = “try to do something”

So:

hún reynir að fá hreyfingu = “she tries to get exercise”
Other examples:
- Hann reynir að læra íslensku. – He tries to learn Icelandic.
- Við reynum að sofa vel. – We try to sleep well.

What does að fá hreyfingu really mean? Literally it looks like “to get movement”.

Literally, yes: að fá hreyfingu = “to get movement”.
Idiomatically, it means “to get some exercise / to be physically active”.

This is a very common way to talk about exercising in an everyday, non-sport-specific sense:

Ég þarf að fá meiri hreyfingu. – I need to get more exercise.
Krakkarnir fengu ekki mikla hreyfingu í dag. – The kids didn’t get much exercise today.

You could also say:

að hreyfa sig – to move / exercise (oneself)
- Hún reynir að hreyfa sig daglega. – She tries to exercise daily.

Both are natural; fá hreyfingu is slightly more idiomatic in this exact sentence.

What form is hreyfingu, and why isn’t it just hreyfing?

Hreyfingu is the accusative singular of hreyfing (feminine noun: movement, exercise).

Nom. sg.: hreyfing – (the) movement/exercise
Acc. sg.: hreyfingu

The verb fá (“to get”) takes its object in the accusative, so you need:

að fá hreyfingu – to get exercise (accusative).

Using the nominative hreyfing here would be ungrammatical.

What does daglega mean exactly, and how is it different from á hverjum degi?

Both mean “every day / daily”, but they’re different in form:

daglega – adverb meaning “daily”, formed from the adjective daglegur (daily, habitual).
- Hún reynir að fá hreyfingu daglega. – She tries to get exercise daily.
á hverjum degi – literally “on each day”.
- Hún reynir að fá hreyfingu á hverjum degi. – She tries to get exercise every day.

They are very close in meaning; daglega is a bit more compact and adverb-like, just like English “daily”.

Can the word order in svo hún reynir að fá hreyfingu daglega be changed?

A little, but the original order is the most natural. Some possibilities:

… svo hún reynir daglega að fá hreyfingu.
→ Also correct; daglega is moved earlier, stressing the trying as a daily effort.

Less natural or odd:

*… svo hún reynir að daglega fá hreyfingu. – sounds awkward.
*… svo hún reynir að fá daglega hreyfingu. – could be understood, but suggests “daily exercise” as a fixed thing, and feels less idiomatic.

The given sentence:

svo hún reynir að fá hreyfingu daglega

is the smoothest and most neutral word order.

Any quick tips for pronouncing Íþróttir hafa góð áhrif á heilsuna hennar?

A few simple pointers (not full phonetics, just practical hints):

Í – like a long “ee” in see.
þ in Íþróttir – like “th” in think (unvoiced).
ó in íþróttir, góð – like a long “o” in go.
Double tt in íþróttir – a strong t sound; don’t make it “tr”.
á in áhrif, á heilsuna – like “ow” in cow, but shorter and cleaner.
heilsu- – roughly “HAYL-suh”.
hennar – roughly “HEN-ar” (both syllables clearly pronounced).

Putting it together slowly and clearly will already get you very close to a natural Icelandic pronunciation.