Ho capito che avevo dimenticato la chiave.

Ho capito is the passato prossimo, and here it means I realized / I understood at a specific moment.

• ho capito = I realized / I understood
• capivo = I was understanding / I used to understand / I understood in an ongoing background sense
• capii = I understood, in the passato remoto, which is mostly used in literature or in some regional spoken Italian, not usually in everyday conversation

In this sentence, the speaker is talking about a completed moment of realization, so ho capito is the natural everyday choice.

Because the forgetting happened before the realization.

The sentence has two past actions:

1. Ho capito = I realized
2. avevo dimenticato la chiave = I had forgotten the key

Italian uses trapassato prossimo for the earlier past action:

• avevo dimenticato = I had forgotten

So the tense relationship is:

• first: I forgot the key
• later: I realized it

If you said Ho capito che ho dimenticato la chiave, it would sound less natural in standard tense sequence, because both actions would be placed at the same general past level. Italian usually prefers avevo dimenticato here.

It is the trapassato prossimo, formed with:

• the imperfetto of the auxiliary verb
• plus the past participle

Here:

• avevo = I had
• dimenticato = forgotten

So:

• avevo dimenticato = I had forgotten

The verb dimenticare uses avere as its auxiliary, so that is why you get avevo, not ero.

Che means that and introduces the subordinate clause.

So:

• Ho capito = I realized
• che avevo dimenticato la chiave = that I had forgotten the key

In English, that is often optional:
I realized (that) I had forgotten the key.

In Italian, che is normally included in this kind of sentence.

Because Italian often leaves out subject pronouns when they are not needed.

Both verbs clearly show the subject is I:

• ho capito = I realized
• avevo dimenticato = I had forgotten

Since the verb endings already tell you the subject, io is unnecessary unless you want emphasis or contrast.

For example:

• Io ho capito che avevo dimenticato la chiave
  = I realized that I had forgotten the key

This sounds more emphatic, as if contrasting with someone else.

In Italian, articles are used more often than in English.

La chiave means the key. Italian normally wants the article here because it refers to a specific key, even if English might sometimes express the idea a little differently depending on context.

So:

• dimenticare la chiave = to forget the key

Leaving out the article would sound wrong in standard Italian.

No. In this sentence, capito does not agree with the subject because it is used with the auxiliary avere.

With avere, the past participle usually stays in its default masculine singular form unless there is a direct object pronoun before the verb that triggers agreement.

So:

• ho capito
• avevo dimenticato

both stay unchanged.

This is true whether the speaker is male or female.

It follows a very normal Italian structure:

• main clause: Ho capito
• subordinate clause introduced by che: avevo dimenticato la chiave

Italian word order is often similar to English here:

• I realized that I had forgotten the key
• Ho capito che avevo dimenticato la chiave

You could sometimes move things around for emphasis, but this version is the most neutral and natural.

Both can work, but they are not always identical in tone.

• Ho capito che avevo dimenticato la chiave = I realized / understood that I had forgotten the key
• Mi sono reso conto che avevo dimenticato la chiave = I realized / became aware that I had forgotten the key

Rendersi conto often sounds a bit more specifically like to become aware of something.
Capire is broader and can mean to understand as well as to realize.

In this sentence, ho capito is perfectly natural.

Yes, that is also possible.

• Ho capito che avevo dimenticato la chiave
• Ho capito di aver dimenticato la chiave

The second version uses di + infinitive:

• di aver dimenticato = to have forgotten

Both are grammatical. The version with che avevo dimenticato is often very clear for learners because it shows the past-in-the-past relationship directly with avevo dimenticato. The di aver dimenticato version is a bit more compact.

In this context, ho capito usually means I realized rather than I understood in the broad intellectual sense.

So the sentence typically suggests a moment like:

• I reached for the door
• then I realized I had forgotten the key

Italian capire can cover both understand and realize, and context tells you which meaning is intended. Here, the combination with che avevo dimenticato la chiave strongly points to realized.