IHS estimates the cost of materials in the Apple Watch (sports edition) to be $81.2 ($83.7 including the cost of the watch production itself). The most expensive component is the flexible OLED display which costs $20.5 - this is the glass covered display. Other components include the CPU ($10.2), the memory ($7.2) and the power management unit ($5.5).
The display is reportedly made by LG Display, and is a 1.34" diagonal panel with a resolution of 272x340 (290 PPI). The display cost includes TPK's ForceTouch layer. In 2014 DisplaySearch estimated the display would cost $27 to produce (assuming 60% yields).
Besides the square flexible OLED, the Watch has a new custom-designed Apple S1 processor, 8GB of storage, NFC, Wi-Fi, Bluetooth, three sensors (Accelerometer, gyroscope and heart rate monitor) and the new Watch OS. There are several Watch editions, ranging from $349 to $17,000. Apple started shipping the Watch on April 24th 2015.
It should be noted that Tim Cook has commented that the component price estimates he has seen are wildly inaccurate.