The abbreviation "btw" stands for "by the way," and is frequently used in text messages and e-mails. This is one of several common abbreviations familiar to many of those who frequently communicate via text message.
Abbreviations such as "btw" became popular during the era when users had to use the 10-letter phone keypad to enter their text messages. Phones came with features designed to make this task easier, but one of the easiest solutions was to invent abbreviations for common words and phrases. With the advent of QWERTY smartphone keyboards, these techniques have become less necessary, but many persist due to convention.