Дело в том, что я забыл проездной дома.

Дело в том, что is a very common Russian expression meaning something like:

• The thing is that...
• The fact is that...
• What happened is that...

It is used to introduce an explanation, often when giving a reason or excuse.

In this sentence, it sets up the explanation for whatever situation is being discussed.

Literally, the words are:

• дело = matter, affair, thing
• в том = in that
• что = that

But you should treat Дело в том, что... as a fixed expression rather than translating each word separately every time.

This comes from the fixed phrase дело в том, что...

Here:

• в requires the prepositional case
• тот becomes том in the prepositional singular

So:

• тот → том
• в том = in that

Even though the literal structure feels unusual in English, in Russian this is just the normal idiomatic pattern.

Because что introduces a subordinate clause.

The sentence is divided into:

• main part: Дело в том
• subordinate clause: что я забыл проездной дома

Russian normally puts a comma before что when it means that and introduces a clause.

So the comma here is standard grammar, not optional.

Забыл is the past tense of the perfective verb забыть.

It is used because the speaker is talking about a completed event: they forgot the pass.

Compare:

• я забыл = I forgot
• я забывал = I used to forget / I forgot at some point (imperfective, less natural here)
• я забываю = I forget / I am forgetting

In this sentence, забыл is the natural choice because it refers to one finished action with a present consequence: the pass is not with the speaker now.

That is how Russian usually forms the past tense.

For many verbs, the past tense is built from the infinitive stem plus -л:

• забыть → забыл (masculine singular)
• забыла (feminine singular)
• забыло (neuter singular)
• забыли (plural)

So я забыл tells us the speaker is masculine. If the speaker were female, it would be я забыла.

Because проездной is often used on its own as a shortened noun.

Originally, it comes from expressions like:

• проездной билет = travel pass

But in everyday Russian, people very often just say:

• проездной

and everyone understands it means a transport pass, transit pass, or travel card.

So here проездной functions like a noun, even though historically it comes from an adjective.

It is in the accusative singular, because it is the direct object of забыл.

The tricky part is that for this word, the accusative singular looks the same as the nominative singular:

• nominative: проездной
• accusative: проездной

That happens because it is inanimate and masculine.

So even though the form does not change, its role in the sentence is still that of a direct object.

Here дома means at home.

This is a very common adverbial use:

• Я дома = I am at home
• забыл дома = left/forgot it at home

Compare:

• дома = at home
• домой = (to) home, toward home
• в доме = in the house/building

So:

• забыл дома = forgot it at home / left it at home

Using домой here would be wrong, because that means motion toward home.
Using в доме would sound more like in the building/house, not the everyday idea of at home.

Yes, literally it is something like forgot [it] at home, but in natural English the idea is usually:

• I left my pass at home
• I forgot my pass at home

Russian often uses забыть in contexts where English might prefer leave behind.

So the sense is: the speaker failed to bring the pass because it remained at home.

Yes. Russian word order is flexible.

The neutral order here is:

• Дело в том, что я забыл проездной дома.

But you could also hear variations such as:

• Я забыл дома проездной.
• Проездной я забыл дома.
• Дело в том, что дома я забыл проездной.

The meaning stays basically the same, but the emphasis changes:

• проездной earlier in the sentence emphasizes the pass
• дома earlier emphasizes where it was forgotten
• Дело в том, что... keeps the sentence sounding like an explanation

Yes, in this sentence it is natural to include я.

Russian often drops subject pronouns when the meaning is obvious, but with past tense forms like забыл, the verb only shows gender and number, not person. So я helps make the subject explicit.

Without я, the sentence could still be possible in context:

• Дело в том, что забыл проездной дома.

But that sounds more conversational and context-dependent.
The version with я is clearer and safer for learners.

It is neutral, everyday Russian.

• Дело в том, что... can sound a bit explanatory or polite
• проездной and дома are completely normal everyday words
• the whole sentence works well in ordinary conversation

It could be said to a friend, a ticket inspector, a coworker, or in many similar situations.

So it is not especially formal, but it is also not slangy.