Especially (cheap) screens used with embedded devices do not provide 24 bit color-depth. Moreover, storing and/or transmitting 3 bytes per pixel is consuming quite some memory and creates latency. RGB565 requires only 16 (5+6+5) bits/2 bytes and is commonly used with embedded screens. It provides 5 bits for Red and Blue and 6 bits for Green. Providing 5 bits for 2 colors and 6 bits for another seems asymmetric but storing and transmitting something which cannot nicely be packed in bytes would be complicated.

Note that since we have less bits (information) available, we can represent less colors. While RGB888 provides 2^24=16 777 216 colors, RGB565 only provides 2^16=65 536 colors.