Learn Russian: Мы знаем, что её алиби — это просто шутка.

In Russian, you must always put a comma before the second part of a sentence introduced by connecting words like что (that), где (where), or когда (when). Unlike in English, where you can often leave out the word 'that' or skip the comma, this comma is a strict rule in Russian punctuation.

Does что mean 'what' or 'that' in this sentence?

Here it means 'that'. While что is the question word for 'what', it is also the main word used for reported statements to connect indirect speech to phrases like мы знаем (we know). And do not forget the pronunciation rule: it is spoken as што.

Why do we use a dash and это instead of a verb for 'is'?

Russian almost always drops the verb 'to be' in the present tense. When equating one noun concept to another (like linking her 'alibi' to being a 'joke'), Russian often uses a long dash and the word это to bridge them together. It acts just like 'is' does in English.

What gender is the word алиби and why does it not have a standard ending?

Алиби is a borrowed foreign word. In Russian, many borrowed nouns ending in vowels like -и, -о, or -е (think of такси or кафе) are indeclinable. This means their spelling never changes regardless of their role in the sentence, and they are usually treated as neuter words.