Forklaringen er overbevisende.

Because Norwegian usually marks definiteness at the end of the noun.

• en forklaring = an explanation
• forklaringen = the explanation

So the -en here is the definite ending. English uses a separate word, the, but Norwegian often attaches that meaning directly to the noun.

For the same reason: Norwegian commonly uses a suffix instead of a separate article.

In English, you say:

• the explanation

In Norwegian, you say:

• forklaringen

So forklaringen already includes the idea of the.

Er means is / are / am, depending on context. It is the present tense of å være, which means to be.

So in this sentence:

• Forklaringen er overbevisende
• The explanation is convincing

Very common forms of å være are:

• er = am / is / are
• var = was / were
• vært = been

Here, overbevisende is a predicate adjective, meaning it comes after er and describes the subject.

Many Norwegian adjectives do change depending on gender and number, but adjectives ending in -ende usually stay the same.

For example:

• en overbevisende forklaring = a convincing explanation
• et overbevisende argument = a convincing argument
• forklaringen er overbevisende = the explanation is convincing
• argumentet er overbevisende = the argument is convincing
• de er overbevisende = they are convincing

So overbevisende is nice and simple: it usually keeps the same form.

It is used here as an adjective, but it is related to the verb å overbevise, which means to convince.

So:

• å overbevise = to convince
• overbevisende = convincing

This is similar to English, where convincing comes from to convince.

In the sentence Forklaringen er overbevisende, it functions as an adjective describing forklaringen.

No. After er, you normally use the adjective directly.

So this is correct:

• Forklaringen er overbevisende

Not:

• Forklaringen er en overbevisende

That would feel incomplete, because en would normally need a noun after it, such as:

• Det er en overbevisende forklaring = It is a convincing explanation

So:

• after er
  • adjective: er overbevisende
• inside a noun phrase: en overbevisende forklaring

Yes, in some varieties of Bokmål, that is possible.

You may see:

• forklaringen
• forklaringa

Both can mean the explanation. The version in your sentence, forklaringen, is very common and perfectly standard.
Forklaringa is used by people who choose feminine forms more actively in Bokmål.

So for a learner, forklaringen is a very safe form to use.

The difference is definite versus indefinite.

• Forklaringen er overbevisende = The explanation is convincing
• En forklaring er overbevisende = An explanation is convincing or One explanation is convincing, depending on context

The first sentence points to a specific explanation.
The second is more general or introduces one explanation among others.

So if you are talking about a particular explanation already known in the conversation, forklaringen is the natural choice.

The sentence follows a very common Norwegian pattern:

• subject + verb + complement

Here that is:

• Forklaringen = subject
• er = verb
• overbevisende = complement

So the structure is very similar to English:

• The explanation is convincing

This is one of the easiest Norwegian sentence patterns for English speakers, because it matches English quite closely.