Az egyéni edzés ma kezdődik.

Hungarian has two forms of the definite article:

• a before consonant sounds
• az before vowel sounds

Since egyéni starts with a vowel, the correct form is az egyéni edzés.

Examples:

• a könyv = the book
• az alma = the apple

Egyéni means individual, personal, or done alone / on one’s own depending on context.

It is related to egy, which means one. So the basic idea behind egyéni is something like individualized or belonging to one person.

In this sentence, egyéni edzés means something like:

• individual training
• personal training
• one-on-one training
  depending on context.

In Hungarian, adjectives usually do not agree with nouns in gender, number, or case the way they do in many Indo-European languages.

So egyéni stays egyéni before the noun:

• az egyéni edzés
• az egyéni órák
• az egyéni program

Unlike in languages such as German or Spanish, the adjective does not get extra endings just because the noun changes.

Edzés is a noun meaning training, practice, or workout, especially in a sports or fitness context.

It comes from the verb edz, meaning to train.

So:

• edzés = training / workout
• egyéni edzés = individual training / personal workout session

Ma means today.

It is an adverb of time, and in this sentence it tells us when the training begins.

So the structure is roughly:

• Az egyéni edzés = the individual training
• ma = today
• kezdődik = starts / begins

Kezdődik means begins or starts in an intransitive sense: the event itself starts.

Compare:

• A film kezdődik. = The film is starting.
• Péter kezdi a munkát. = Péter starts the work.

So:

• kezd is often used when someone starts something
• kezdődik is often used when something begins by itself or gets underway

In your sentence, the training session is what begins, so kezdődik is natural.

The dictionary form here is kezdődik, which belongs to the group of Hungarian verbs often called -ik verbs.

In modern everyday Hungarian, this mostly matters in certain forms and in dictionary listings, but for a learner, the most important thing here is simply:

• kezdődik = it begins / it starts

You do not need to think of the -ik here as a separate ending with a simple one-word English equivalent. It is just part of the verb’s standard form.

Hungarian word order is quite flexible, and different orders can change the emphasis.

Az egyéni edzés ma kezdődik. is a natural sentence meaning:

• The individual training starts today.

Other possible orders include:

• Ma kezdődik az egyéni edzés.
  This puts more emphasis on today.

• Az egyéni edzés kezdődik ma.
  This is possible, but less neutral in many contexts.

Hungarian word order is strongly connected to topic and focus, not just grammar. The original sentence is a good neutral pattern.

Hungarian often uses the definite article where English may or may not use the, depending on style and context.

Here, Az egyéni edzés suggests a specific training session, program, or known type of training that both speaker and listener understand.

So it feels like:

• the individual training
• that personal training session

If you removed the article, the sentence would sound different and less natural in many ordinary contexts.

Yes. Kezdődik is present tense: starts / is starting / begins.

Hungarian often uses the present tense for near-future meaning, just like English can:

• The class starts today.
• The train leaves at six.

So Az egyéni edzés ma kezdődik is present tense in form, but it can refer to something beginning later today.

A rough pronunciation guide is:

az edy-AY-nee ED-zhesh ma KEZ-dur-deek

A few helpful notes:

• gy is a soft sound, somewhat like the d in British duke or a softened dy
• é is a long ay sound
• zs sounds like the s in measure
• ő is a long rounded vowel not found in English; you may approximate it at first
• stress in Hungarian usually falls on the first syllable of each word:
  • AZ
  • E-gyé-ni
  • ED-zés
  • MA
  • KEZ-dő-dik

Yes. Even if the basic meaning is clear, the exact nuance depends on the situation.

It could mean:

• an individual workout
• personal training
• a one-on-one session
• training done alone rather than in a group
• a customized training program

So the Hungarian phrase is broad enough to cover several related English expressions. The context tells you which shade is meant.