The letter “Ы” is so special that it deserves a separate journal entry. It looks like two characters, and represents a sound that many languages (English, French, German, Spanish and so on) don't have. It is extremely difficult to explain to non-native speakers how to pronounce “ы”, but anyway, this letter is very important in Russian.
As you may know, all Russian consonants can be categorized into soft (palatalized) and hard (non-palatalized) sounds. The bad news is that both palatalized and non-palatalized sounds are represented by same characters. The only way to guess if the consonant sound is hard or soft is to take a look at the next vowel. If it is а/о/у/э/or ы, then the preceding consonant is hard. If it is я/ё/ю/е/ or и, the consonant is soft. The vowel letter group “softens” the preceding consonants. The vowel “Ы” shows that the preceding consonant sound is hard. Phonologically speaking, the only difference between Ы and И is that И follows a soft consonant, and Ы follows a hard consonant.
Why pay attention to all (of) this stuff with hard and soft sounds? Because there are many words that only differ by one letter ы/и, for example:
бить (to beat) — быть (to be),
вить (to weave) — выть (to howl),
следи (watch, imperative)— следы (footprints),
грози (threaten, imperative)́ — грозы́ (thunderstorms),
клик (a click)— клык (a fang),
мило (nice) — мыло (soap),
сосни́ (suck, imperative) — сосны́ (pine trees)
пил (drunk, past simple) — пыл (heat, passion),
сгори (may you burn) — с горы (from the mountain),
ти́кать (to tick) — ты́кать (to poke)
The most popular cultural reference to the letter “Ы” is from a famous Soviet comedy “Operation Y and Other Shurik's Adventures” by Leonid Gaigai (Операция „Ы“ и другие приключения Шурика). The movie consists of three parts, each of them a story about the adventures of Shurik (alternative spelling — Shourick), the naive and nerdy Soviet student who often gets into ludicrous situations but always finds a clean way out. The third story, titled “Operation Y,” is about three criminals hired to simulate a burglary in order to cover for the overembezzling of a warehouse manager. One of the criminals offered to call the fake burglary “Operation Y” for conspiracy reasons. Watch the entire movie, and you'll be more familiar with modern Russian culture. “Operation Y and Other Shurik's Adventures” is a film with jokes and lines often quoted and referenced even nowadays.