tugi ha watasi no ban desu.

It is read:

つぎ は わたし の ばん です。

Word by word:

• 次 = つぎ
• は = written ha but pronounced wa here
• 私 = わたし
• の = no
• 番 = ばん
• です = desu (the u is often very light)

When は is used as the topic particle, it is pronounced wa.

So in this sentence:

• 次は = As for next...

This is one of the first pronunciation exceptions learners meet in Japanese. The spelling stays は, but the pronunciation changes to わ when it functions as a particle.

は marks the topic of the sentence.

So 次は means something like:

• As for next, ...
• Next, ...

It sets up 次 as the thing being talked about. The rest of the sentence tells you what is true about that topic:

• 次は = As for next
• 私の番です = it is my turn

A very literal interpretation would be:

As for next, it is my turn.

私の番 means my turn.

Breakdown:

• 私 = I / me
• の = shows possession or connection
• 番 = turn

So:

• 私の番 = my turn

Here, の works a lot like 's or of in English.

In this sentence, 番 means turn.

Examples of this use:

• 私の番 = my turn
• あなたの番 = your turn
• 次は田中さんの番です = next, it is Tanaka's turn

But 番 can appear in other contexts too, so it does not always translate exactly the same way in every sentence. Here, the idea is clearly whose turn it is.

の links one noun to another.

Here it connects:

• 私
  • 番

So 私の番 means my turn, just like:

• 私の本 = my book
• 彼の車 = his car

Without の, 私番 would be ungrammatical.

です makes the sentence polite and completes it in a standard way.

You can think of it as similar to saying:

• It is my turn
• rather than just
• My turn

So:

• 私の番です = It is my turn

In casual speech, people might say:

• 次は私の番だ
• or even just 次は私の番

But です is the normal polite ending.

次は私です is possible, but it is slightly different in nuance.

• 次は私です = I’m next
• 次は私の番です = It’s my turn next / I’m up next

私の番です focuses more clearly on the idea of turn-taking.
So if people are taking turns in a game, speech, performance, or line, 番 makes that meaning very natural.

Yes, you could say there is an implied it in English.

Japanese often leaves out things that are understood from context. So the sentence does not explicitly say it, but English usually needs something like:

• Next, it is my turn
• I’m next

Japanese does this all the time. If the context is clear, subjects and objects are often omitted.

Japanese normally does not use spaces like this in regular writing.

The standard writing would be:

次は私の番です。

Spaces are often added in beginner materials to make the sentence easier to read and to show where the parts are.

Yes. 次 generally refers to the next thing in order.

Depending on context, it can mean:

• next in a sequence
• next person
• next event
• after this

In 次は私の番です, it means next in turn/order.

A useful breakdown is:

• 次は = as for next
• 私の番 = my turn
• です = is / polite ending

So a very literal gloss is:

As for next, it is my turn.

That is not the most natural English sentence, but it shows the Japanese structure clearly.