Trebalo bi da danas odem u poštu, jer moram da pošaljem paket.

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Breakdown of Trebalo bi da danas odem u poštu, jer moram da pošaljem paket.

• danas: today
• morati: must
• jer: because

Questions & Answers about Trebalo bi da danas odem u poštu, jer moram da pošaljem paket.

What does trebalo bi da mean here?

It means should or ought to.

So Trebalo bi da danas odem u poštu means something like I should go to the post office today.

It sounds softer than a direct obligation. In the same sentence, moram da pošaljem paket is stronger: I have to send a package. So the logic is:

• trebalo bi = recommendation / sensible thing to do
• moram = real necessity

That is why the sentence feels natural:
I should go to the post office today, because I have to send a package.

Why is it trebalo bi and not trebao bih?

Both are possible, but they work a little differently.

• Trebalo bi da odem = an impersonal, very common way to say I should go
• Trebao bih da odem = a more personal form, also meaning I should go

With trebao bih / trebala bih, the form agrees with the speaker’s gender:

• trebao bih = if the speaker is male
• trebala bih = if the speaker is female

But trebalo bi stays neutral and is extremely common in everyday Serbian.

So:

• Trebalo bi da danas odem u poštu.
• Trebao bih da danas odem u poštu.
• Trebala bih da danas odem u poštu.

All can mean basically the same thing.