This pattern literally means 'to do the appearance of', so it's used when someone acts as if something is true when it isn't. It works with verbs (dictionary or past form) and with nouns/な-adjectives using の. The verb form shows what the pretense is about: present for current actions or states, past for things that supposedly happened earlier. You'll hear it in everyday conversation, often with 知らないふり (pretending not to know) or 寝たふり (pretending to be asleep).

A common nuance is that the pretense is intentional and often to avoid trouble or responsibility. It can be used for harmless play-acting too, like pretending to be a monster with a child. The tone is neutral, but using it about yourself often implies a bit of embarrassment or self-awareness. For example, 知らないふりをした means 'I pretended not to know' — maybe to avoid getting involved.

Formality: It's standard and works in both speech and writing, but it's more common in casual conversation. In very formal contexts, you might use ふりをする with ます form or other polite structures, but the pattern itself is not rude.