V lednici máme vejce, máslo, sýr a pomeranče, ale nemáme banány.

Because v meaning in takes the locative case when it expresses location.

The base form is lednice = fridge.
Its locative singular form is lednici.

So:

• lednice = fridge
• v lednici = in the fridge

V and ve both mean in. Ve is just a pronunciation variant used when v would be awkward to say before certain sounds or consonant clusters.

For example:

• ve škole = in the school
• ve středu = on Wednesday

But v lednici is easy to pronounce, so plain v is the normal form.

Because Czech often leaves out subject pronouns when the verb already makes the meaning clear.

Máme already means we have, so adding my = we is usually unnecessary.

• máme = we have
• nemáme = we do not have

You could say my máme for emphasis, but in a neutral sentence it is normally omitted.

Because Czech very often uses mít = to have when talking about what is available or what someone has in a place such as a fridge, bag, house, or room.

So V lednici máme... is a very natural way to say that these things are in our fridge.

A sentence with jsou = are is also possible:

• V lednici jsou vejce...

That version sounds a bit more like a neutral description of what is there.
Máme feels more like we have these things available.

Nemáme is simply the negative form of máme.

Czech usually makes a verb negative by adding ne- to it:

• máme = we have
• nemáme = we do not have / we don’t have

So:

• máme vejce = we have eggs
• nemáme banány = we do not have bananas

Because Czech has no articles.

English needs words like a, an, and the, but Czech does not. The exact meaning is understood from context.

So:

• vejce can mean eggs, the eggs, or some eggs
• banány can mean bananas, the bananas, or some bananas

In this sentence, the general meaning is simply understood from the situation.

They are the direct objects of máme / nemáme, so they are in the accusative case.

In this sentence, many of those accusative forms happen to look the same as the basic dictionary form:

• vejce — neuter, same form in nominative and accusative
• máslo — neuter, same form in nominative and accusative
• sýr — masculine inanimate singular, accusative = nominative
• pomeranče — masculine inanimate plural, accusative plural = nominative plural
• banány — masculine inanimate plural, accusative plural = nominative plural

So even though they are objects, you do not see a big form change here.

In form, vejce can be tricky because the nominative/accusative singular and nominative/accusative plural are both vejce.

So the form itself does not tell you everything.

In this sentence, it is understood as eggs from the context — a list of food items in the fridge. Czech often uses vejce in this practical, grocery-list kind of way.

Because ale means but, and in Czech it normally introduces a new clause, so it is preceded by a comma.

So:

• V lednici máme vejce, máslo, sýr a pomeranče, ale nemáme banány.

Notice that there is no comma before a in the simple list:

• vejce, máslo, sýr a pomeranče

That works the same way as English eggs, butter, cheese, and oranges, except Czech usually does not use the extra final comma there.

Because Czech word order is flexible, and speakers often move something to the front to make it the topic or setting.

Starting with V lednici gives the location first:

• As for the fridge, we have...

This is completely natural.

You could also say:

• Máme v lednici vejce, máslo, sýr a pomeranče...

That is also correct, but the emphasis is a little different. The version with V lednici first highlights the place more strongly.

Here ale means but.

It connects two contrasting ideas:

• we have eggs, butter, cheese, and oranges
• but we do not have bananas

So ale marks a contrast between what is available and what is missing.