Vid stranden hade vi varsina muggar, men bara ett stort glas till juicen.

Vid stranden literally means by the beach / by the shore / at the shore.

• vid = by, next to, at
• stranden = the beach / the shore

In natural English, this might sometimes be translated as at the beach, even though Swedish is more literally by the shore.

A learner might expect på stranden, which means more specifically on the beach.
So:

• vid stranden = near the shoreline / by the beach
• på stranden = physically on the beach

Both can be possible in different contexts, but vid focuses more on location beside something.

This is because Swedish follows the V2 rule in main clauses: the finite verb must come in the second position.

In this sentence, Vid stranden has been placed first for emphasis or scene-setting. When that happens, the verb must come next:

• Vid stranden = first position
• hade = second position
• vi = after the verb

So:

• Vid stranden hade vi varsina muggar ... = correct
• Vi hade varsina muggar vid stranden ... = also correct, but with a different emphasis

Both are grammatical. The given version starts by setting the scene: At the beach / By the shore...

Varsina means something like one each, each their own, or a separate one for each person.

So vi hade varsina muggar means:

• we each had our own mug
• literally: we had one mug each

This word is very useful in Swedish and does not translate neatly into one single English word.

Related forms are:

• varsin — used with common-gender singular nouns
• varsitt — used with neuter singular nouns
• varsina — used with plural nouns

Both can express a similar idea, but the form depends on the noun structure.

In the sentence, muggar is plural, so Swedish uses varsina:

• varsina muggar = one mug each

You could also say:

• vi hade varsin mugg

That also means we each had a mug.

So why use the plural version here? Because Swedish allows this distributive pattern with a plural noun:

• varsin mugg = each person had one mug
• varsina muggar = each person had their own mugs, understood as one each in this context

Both are natural, though varsin mugg may feel a little more straightforward to learners.

They are two different kinds of drinking containers:

• mugg = mug or sometimes cup, usually not transparent
• glas = drinking glass

So in the sentence:

• varsina muggar = separate mugs for each person
• ett stort glas = one large drinking glass

Note that glas can also mean glass as a material, but here it clearly means a drinking glass.

Because glas is an ett-word in Swedish.

That affects both the article and the adjective:

• ett glas = a glass
• ett stort glas = a big glass

The adjective stor becomes stort with an ett-word singular noun.

Compare:

• en stor mugg = a big mug
• ett stort glas = a big glass

So this is standard adjective agreement.

It can be understood as both, depending on context.

• ett glas can mean a glass
• it can also mean one glass

In this sentence, because of bara (only), English naturally understands it as only one big glass.

So:

• bara ett stort glas = only one big glass

Even though ett is also the normal indefinite article for neuter nouns, the context makes the number idea stronger here.

Bara means only / just.

Here it limits ett stort glas:

• men bara ett stort glas = but only one big glass

It contrasts with the first part of the sentence:

• everyone had their own mugs
• but there was only one large glass for the juice

So bara highlights a shortage or limitation.

Here till means something like for.

So:

• ett stort glas till juicen = a big glass for the juice

This use of till often shows intended use or what something goes with.

Examples:

• en sked till soppan = a spoon for the soup
• ett lock till burken = a lid for the jar
• ett glas till juicen = a glass for the juice

It is not about movement here. It does not mean to the juice in a literal direction sense.

Juicen is the definite form: the juice.

Swedish often uses the definite form where English might or might not use the, depending on context. Here it refers to a specific juice already understood in the situation.

• juice = juice
• juicen = the juice

So till juicen means for the juice.

If you said till juice, that would sound more general or less natural in this context.

Here hade is simply the past tense of ha (to have), so it means had.

• ha = to have
• hade = had

The sentence is describing what the group possessed or had available at that time:

• we had our own mugs
• but only one large glass for the juice

So there is no special idiomatic meaning here; it is an ordinary past-tense use of ha.

Yes. A very natural alternative would be:

• Vi hade varsina muggar vid stranden, men bara ett stort glas till juicen.

This version starts with vi instead of vid stranden.

The difference is mainly emphasis:

• Vid stranden hade vi ... = starts by setting the scene
• Vi hade ... vid stranden = starts with the people and what they had

Both are grammatical. The original version feels a bit more narrative or descriptive.

These forms agree with the noun, much like adjectives do.

Use:

• varsin with en-words in singular
  
  • varsin mugg = one mug each
• varsitt with ett-words in singular
  
  • varsitt glas = one glass each
• varsina with plural nouns
  
  • varsina muggar = one mug each / their own mugs

So in your sentence, muggar is plural, which is why the form is varsina.

This is one of those Swedish patterns that English usually expresses with a phrase instead of a single word.