Die Dozentin sagt, ein Doppelpunkt passe gut, wenn danach eine Erklärung kommt.

Dozentin is a feminine noun meaning female lecturer or female instructor. Because it is feminine, it takes the feminine definite article die in the nominative singular:

• der Dozent = the male lecturer
• die Dozentin = the female lecturer

Here Die Dozentin is the subject of the sentence, so nominative is needed.

The comma separates the main clause from the following reported statement.

• Main clause: Die Dozentin sagt
• Reported content: ein Doppelpunkt passe gut, wenn danach eine Erklärung kommt

In German, commas are used much more systematically than in English to mark clause boundaries, so this comma is normal and required.

German often allows two ways to introduce reported content after verbs like sagen:

1. with dass
   Die Dozentin sagt, dass ein Doppelpunkt gut passt ...

2. without dass, often using Konjunktiv I
   Die Dozentin sagt, ein Doppelpunkt passe gut ...

The version without dass is common in more formal or report-like style, especially when reporting someone’s words or opinion.

Passe is Konjunktiv I of passen. German uses Konjunktiv I very often in indirect or reported speech.

So:

• passt = normal present tense
• passe = reported-speech form

Using passe signals something like: this is what the lecturer says.

That is why the sentence sounds a bit more formal or careful than everyday speech.

Yes. In everyday German, many people would say:

Die Dozentin sagt, ein Doppelpunkt passt gut, wenn danach eine Erklärung kommt.

That is very natural in conversation.
The version with passe is simply more explicitly marked as reported speech.

So the difference is mostly about style and nuance, not basic meaning.

Because ein Doppelpunkt is the subject of the clause, so it is in the nominative case.

• nominative masculine: ein Doppelpunkt
• accusative masculine: einen Doppelpunkt

Here the structure is basically:

ein Doppelpunkt + passe

So ein Doppelpunkt is the thing that fits/works well, which makes it the subject.

Because gut is an adverb here, not an adjective before a noun.

It modifies the verb passe:

• gut passen = to fit well / to work well

Adverbs in German do not take adjective endings.

Compare:

• ein guter Doppelpunkt = a good colon → adjective before a noun
• ein Doppelpunkt passt gut = a colon works well → adverb modifying the verb

Because wenn introduces a subordinate clause, and in German subordinate clauses send the finite verb to the end.

So:

• main clause word order: Eine Erklärung kommt danach
• subordinate clause: wenn danach eine Erklärung kommt

This verb-final pattern is one of the most important German word-order rules.

It can be understood either way, and that is very normal in German.

Wenn can mean:

• if in a conditional sense
• when in a general/repeated sense

In this sentence, the idea is something like:

• a colon works well if an explanation follows
• a colon works well when an explanation follows

Both fit the context. English often forces you to choose more clearly than German does.

Danach means after that or after it.

In this sentence, it refers to what comes after the colon. So:

wenn danach eine Erklärung kommt
= when/if an explanation comes after it

Here it refers to the Doppelpunkt.

So the sentence is talking about punctuation: a colon works well when an explanation follows it.

German often places time or position words early in the clause. In the subordinate clause, danach comes before the subject eine Erklärung:

wenn danach eine Erklärung kommt

That word order is completely normal. You could think of it as emphasizing what happens after that.

The clause structure is:

• wenn = subordinating conjunction
• danach = adverb
• eine Erklärung = subject
• kommt = finite verb at the end

So nothing unusual is happening; it is standard German word order.