Mióta elkezdődött a tanfolyam, jobban értem a záridőt.

Here mióta introduces a time clause meaning since: it gives the starting point from which the situation in the main clause has been true.

So Mióta elkezdődött a tanfolyam means since the course started.

A learner should also know that mióta? can be a question word meaning since when? / how long?
You will also often see amióta in statements with the same function, for example Amióta elkezdődött a tanfolyam....

Because Mióta elkezdődött a tanfolyam is a subordinate clause, and Hungarian normally separates a subordinate clause from the main clause with a comma.

So the structure is:

• Mióta elkezdődött a tanfolyam = subordinate time clause
• jobban értem a záridőt = main clause

This comma is standard in Hungarian.

It is made from:

• kezdődik = to begin / to start
• el- = a verbal prefix

Hungarian verbal prefixes are often written together with the verb in a neutral affirmative sentence, so:

• elkezdődött = started / began

A useful thing to notice: the prefix can separate in some environments, for example after nem or in certain focused structures:

• nem kezdődött el = did not start

Because here the course is the thing that started.

• A tanfolyam elkezdődött = The course started / began
• Valaki elkezdte a tanfolyamot = Someone started the course

So:

• elkezdődött is the intransitive form: the subject itself begins
• elkezdte is transitive: someone starts something

Hungarian usually leaves subject pronouns out when the verb ending already shows who the subject is.

Here értem already tells you the subject is I.

So Hungarian does not need én unless you want emphasis or contrast:

• Én jobban értem a záridőt. = I understand the shutter speed/deadline better (with emphasis on I)

Because Hungarian has two kinds of verb conjugation: indefinite and definite.

Here the object is a záridőt, which is definite, so the verb takes the definite conjugation:

• értem = I understand it/the definite thing
• értek = I understand with no definite object, or with an indefinite object

So the sentence uses:

• értem a záridőt

not

• értek a záridőt

Because it is the direct object of the verb, so it takes the accusative ending -t.

• záridő = base form
• záridőt = accusative form, the záridő as the thing being understood

This is a very common Hungarian pattern: direct objects usually get -t.

jobban is the comparative adverb meaning better.

It comes from the irregular pair:

• jó = good
• jól = well
• jobb = better
• jobban = better (used adverbially, as in understand better)

So:

• jobban értem = I understand better

Because Hungarian often uses the present tense in the main clause to describe a situation that is true now, even if it began because of something in the past.

So the idea is:

• the course started in the past
• as a result, now I understand it better

Hungarian does not need a special present perfect form here. The time relationship is already clear from mióta elkezdődött.

a / az is the Hungarian definite article, equivalent to the.

It is a here because both following words begin with a consonant:

• a tanfolyam
• a záridőt

The article is used because both nouns are understood as specific. Also, the definiteness of a záridőt is exactly why the verb is értem and not értek.

To some extent, yes. Hungarian word order is flexible, and different orders can shift emphasis.

This sentence begins with the time clause:

• Mióta elkezdődött a tanfolyam, ...

That is natural because it sets the time frame first.

Also, jobban appears before the verb, which is very common when that element is prominent:

• jobban értem

You could also hear other orders in context, but they may sound different in emphasis. Hungarian word order is not random; it often reflects what is being highlighted.