Learn Russian: Мне нравится один город, а именно Казань.

Not exactly. In this context, один functions more like the English phrases 'a certain' or 'some'. It is commonly used in Russian to introduce a specific but previously unidentified thing right before the speaker reveals its name.

How does the phrase а именно work, and why is the conjunction а necessary?

The phrase а именно is a set expression meaning namely or specifically, used to introduce a clarification or a list. While именно by itself means exactly, the conjunction а is required in this phrase to bridge the general category (один город) with the specific clarification (Казань).

Why is Казань in the nominative case here instead of the accusative?

With the verb нравиться, the person who likes something is in the dative case (Мне), and the thing being liked is the grammatical subject in the nominative case (город). Because Казань is simply renaming or identifying that subject, it matches its case and also stays in the nominative.

I see that Казань ends in a soft sign (-ь). Is it a masculine or feminine noun?

Казань is feminine. While nouns ending in a soft sign can be either masculine or feminine, a helpful trick is that almost all Russian cities ending in a soft sign (like Казань, Пермь, and Тверь) are feminine.