Religio matrem ad templum ducit, ut votum solvat.

Because religio is in the nominative singular, which is the case normally used for the subject of a Latin sentence.

The verb ducit is third person singular, so we look for a singular nominative noun to go with it. Religio matches perfectly: religio ... ducit = religion/religious devotion leads.

A learner may notice that in English religion is usually an abstract idea, but Latin often allows abstract nouns to act very naturally as subjects. So religio can mean something like religious duty, scruple, conscience, or piety, depending on context.

Because matrem is the direct object of ducit.

The verb ducere means to lead or to bring, and the person being led is put in the accusative case:

• matrem = mother as the object
• ducit = leads

So matrem ducit means leads the mother.

Its dictionary form is mater, but here it appears as matrem because of its role in the sentence.

Ad templum means to the temple.

The preposition ad regularly takes the accusative case when it means to, toward, or up to. So:

• ad = to / toward
• templum = accusative singular of templum

This is a different use of the accusative from matrem:

• matrem is accusative because it is the direct object
• templum is accusative because it follows the preposition ad

So Latin can have two accusatives in one sentence for different reasons.

Here ut introduces a purpose clause.

A purpose clause explains why something is done:

• ducit = leads
• ut votum solvat = so that she may fulfill/pay her vow

So the idea is: Religio matrem ad templum ducit, ut votum solvat
= Religious duty leads the mother to the temple so that she may fulfill her vow.

When you see ut followed by a subjunctive verb, one very common possibility is a purpose clause.

Because after ut in a purpose clause, Latin normally uses the subjunctive.

So:

• solvit would be indicative: she pays / fulfills
• solvat is subjunctive: that she may pay / fulfill, or more naturally in English here, so that she may fulfill

This is standard Latin grammar:

• ut
  • subjunctive = often purpose
• main verb in present tense (ducit) + subjunctive in present tense (solvat) = sequence that fits a present-time purpose

The understood subject of solvat is most naturally the mother.

Latin often leaves out subject pronouns when they are clear from context. Since matrem is the person being taken to the temple, and since fulfilling a vow is something a person does there, the natural understanding is:

• Religio leads the mother to the temple
• so that she may fulfill the vow

So although Latin does not say ea solvat, the subject is understood from the context.

Votum solvere is an important Latin expression meaning to fulfill a vow, to pay a vow, or to discharge a vow.

Literally:

• votum = vow
• solvere = to loosen, release, pay, fulfill

In religious contexts, solvere votum means carrying out what was promised to a god. So if someone made a vow and then went to a temple to complete it, Latin can say votum solvit.

This is more idiomatic than translating word-for-word as loosens a vow.

Latin word order is more flexible than English word order because Latin uses case endings to show grammatical roles.

In English, word order usually tells us who is doing what:

• The mother leads religion means something different from
• Religion leads the mother

But in Latin, endings already show the roles:

• religio = nominative subject
• matrem = accusative object

That means Latin can arrange words for emphasis or style. This sentence is still fairly straightforward, but it does not need to follow strict English-style order.

Yes. Religio is one of those Latin words whose meaning depends a lot on context.

Possible shades of meaning include:

• religion
• reverence
• scruple
• sense of religious duty
• piety

In this sentence, religious duty or religious devotion may sound more natural than the modern abstract English word religion. That is because religio here is acting like an inner force that motivates the mother.

In this sentence it is best understood as a purpose clause, not a result clause.

Why?

• The main idea is that religio leads the mother to the temple
• The ut clause gives the intended goal: so that she may fulfill the vow

A result clause usually describes what actually happens as a consequence, often with some sign in the main clause such as tam, ita, sic, or similar wording. None of that is present here. The sentence strongly suggests intention or purpose.

They are:

• religio, religionis — a feminine noun meaning religion, religious duty, scruple
• mater, matris — mother
• templum, templi — temple
• duco, ducere, duxi, ductum — lead
• ut — so that, in order that
• votum, voti — vow
• solvo, solvere, solvi, solutum — loosen, pay, fulfill

These dictionary forms are useful because the actual words in the sentence are inflected:

• matrem comes from mater
• ducit comes from duco
• solvat comes from solvo

A natural translation would be:

Religious devotion leads the mother to the temple so that she may fulfill her vow.

Other possible translations, depending on how you take religio, are:

• Religious duty leads the mother to the temple to fulfill her vow.
• Piety leads the mother to the temple so that she may pay her vow.

The best choice depends on how literal or how natural you want the English to sound.