Við setjum afgangana í ílát og geymum þá í ísskápnum.

Because they are both first-person plural present-tense verb forms: the we forms.

• við setjum = we put
• við geymum = we store / keep

The infinitives are:

• setja = to put
• geyma = to store, keep

A very common pattern in Icelandic is that the við form in the present ends in -um.

Because it is the direct object of setjum, and it is also definite: the leftovers.

The noun is:

• afgangur = a leftover, remainder

In practice, Icelandic often uses the plural for food leftovers:

• afgangar = leftovers

In this sentence, the form becomes afgangana because it is:

• plural
• definite
• accusative (the case used here for the direct object)

So afgangana means the leftovers.

Because þá is the correct pronoun form for them here.

It refers back to afgangana, and it has to match that noun in:

• number: plural
• gender: masculine
• case: accusative

So:

• þeir = they (nominative)
• þá = them (accusative, masculine plural)
• þeim = to them / for them / with them (dative)

Since geymum takes a direct object, Icelandic uses the accusative, so þá is the right form.

Because the second verb, geymum, still needs an object: store them.

English works the same way here:

• We put the leftovers in a container and store them in the fridge.

You would not normally say:

• We put the leftovers in a container and store in the fridge

unless the object were understood from a very specific context.

So Icelandic naturally says:

• setjum afgangana ... og geymum þá ...

The pronoun prevents ambiguity and makes the sentence complete.

Because Icelandic í can mean both, depending on the case that follows it.

A useful rule is:

• í + accusative = into something, with movement
• í + dative = in something, location

So here:

• setjum afgangana í ílát = we put the leftovers into a container
• geymum þá í ísskápnum = we store them in the fridge

This is a very important Icelandic pattern.

Because the nouns are in different cases and also have different definiteness.

• í ílát: after a motion idea (put into), í takes the accusative
• í ísskápnum: after a location idea (store in), í takes the dative

Also:

• ílát is indefinite here: a container
• ísskápnum is definite: the fridge

One extra detail: ílát is a neuter noun whose nominative and accusative forms look the same, so you do not see an obvious ending change there.

Because Icelandic usually puts the definite article onto the end of the noun instead of using a separate word.

So:

• afgangana = the leftovers
• ísskápnum = the fridge (in the dative form)

This is one of the big differences from English.
Instead of a separate the, Icelandic often uses a suffixed article.

Because Icelandic does not have an indefinite article like English a/an.

So a bare noun can mean:

• container
• a container

depending on context.

That is why í ílát is naturally translated as into a container, even though there is no separate word for a.

The form ílát can be a little tricky because it can look the same in more than one form.

In this sentence, it is most naturally understood as:

• a container

But the written form ílát itself does not by itself clearly show singular vs. plural in nominative/accusative. Context tells you what is meant.

So this is one of those cases where English forces a choice that Icelandic may leave more open on the surface.

Because the subject we applies to both verbs.

So:

• Við setjum ... og geymum ...

means:

• We put ... and store ...

This is normal in both Icelandic and English: once the subject has been established, it does not need to be repeated before the second coordinated verb.

You could repeat við for emphasis, but it is not necessary here.

In other sentences, yes, þá can mean then. But not here.

Here, þá is clearly a pronoun meaning them, because it comes right after geymum and refers back to afgangana.

So in this sentence:

• geymum þá = store them

not:

• store then

The grammar and the context make that clear.