Ancilla massam diu subigit, ut panis mollior fiat.

Because ancilla is the subject of the main verb subigit. It means the slave-girl / maidservant, and in this sentence she is the one doing the action.

• ancilla = nominative singular
• it answers who is kneading/working the dough?

So ancilla is nominative because it is the subject.

Because massam is the direct object of subigit. It is the thing being worked on.

• massa = dough lump, mass, dough
• massam = accusative singular

In other words:

• the maidservant does the action
• the dough receives the action

That is why Latin uses the accusative here.

Here subigit means something like works, kneads, or works over the dough.

The verb is subigō, subigere, subēgī, subāctum. In cooking contexts, it can mean to knead dough thoroughly.

Formally, subigit is:

• 3rd person singular
• present tense
• active voice
• indicative mood

So it means she kneads or she is kneading.

Diu is an adverb meaning for a long time or for a long while.

It modifies subigit, telling us how long the action goes on:

• Ancilla massam diu subigit
• The maid kneads the dough for a long time

It is not an adjective, and it does not change its ending.

Here ut introduces a purpose clause. It tells us why the maid kneads the dough for a long time.

• ut panis mollior fiat = so that the bread may become softer

So the structure is:

• main clause: Ancilla massam diu subigit
• purpose clause: ut panis mollior fiat

A very common Latin pattern is:

• ut
  • subjunctive = in order that / so that

Because it is in a purpose clause introduced by ut.

In Latin, purpose clauses normally use:

• ut
  • subjunctive for a positive purpose
• nē
  • subjunctive for a negative purpose

So fiat is subjunctive because the sentence is expressing an intended result or goal:

• she kneads the dough for a long time
• so that the bread may become softer

Fiat is from fīō, fierī, factus sum, meaning become, be made, or sometimes happen.

Here it means may become.

Because the idea is not just the bread is softer, but the bread becomes softer.

• esse means to be
• fieri often means to become or to come to be

So:

• panis mollior est = the bread is softer
• panis mollior fiat = the bread may become softer

Latin uses fiat to show change of state.

Mollior is the comparative form of mollis, meaning soft.

• mollis = soft
• mollior = softer

The point is that kneading the dough for a long time will make the bread softer than before. Latin often uses the comparative even when English might simply say soft enough or softer depending on context.

Here mollior agrees with panis:

• panis = nominative singular masculine
• mollior = nominative singular masculine/feminine comparative form

Because panis is the subject of fiat in the ut clause.

In the purpose clause, the bread is the thing that becomes softer:

• panis = the bread
• fiat = may become
• mollior = softer

So panis is not the object of the main verb subigit. The maid is not kneading the bread itself in this sentence; she is kneading the dough, with the goal that the bread may later become softer.

Because the clause expresses the intended final result.

The maid is kneading the dough now, but the goal concerns the bread that will come from that dough. Latin is looking ahead to the finished product:

• present action: working the dough
• intended result: softer bread

So the sentence is very natural: the dough is what she kneads, but the bread is what will turn out better.

Panis is:

• nominative singular
• masculine

It belongs to the 3rd declension:

• nominative singular: panis
• genitive singular: panis

That identical nominative and genitive form can be confusing for learners, but here the syntax shows it is nominative, because it is the subject of fiat.

Not especially. Latin word order is more flexible than English word order because the endings show the grammatical roles.

This sentence is arranged quite naturally:

• Ancilla = subject first
• massam = object next
• diu subigit = adverb + main verb
• ut panis mollior fiat = purpose clause at the end

English depends heavily on word order, but Latin can move words around for emphasis without changing the core meaning.

Yes. Depending on how literal you want to be, you could translate it as:

• so that the bread may become softer
• in order that the bread may be softer
• so that the bread turns out softer

The grammar is the same in each case: it is a purpose clause with ut and the subjunctive.

Fiat is present subjunctive.

It is used because the main verb subigit is also present, and Latin normally uses the present subjunctive in a purpose clause after a present-tense main verb. This follows the usual sequence of tenses for purpose clauses.

So:

• subigit = present indicative
• fiat = present subjunctive

That combination is exactly what we expect here.