Sensitivity is the efficiency with which an earphone driver uses the power it receives to convert an electrical signal into an acoustical signal, resulting in clear sound without any distortion.
Measured in decibels of sound pressure levels, it indicates the magnitude of loudness which can be achieved at a certain level of power from the source, usually 1 mili watt. Headphones usually have sensitivity ranging within 90-110db/mW so as to avoid volume decibel levels where music listening might become very painful. If you look at the image on the left, you'll be able to judge how loud you'd like your music to be and what sensitivity levels are more suitable.
Higher sensitivity guarantees better driver performance without using a lot of power; however it also means there are chances of distortion at higher volumes(which might cause damage to the earphone and your ears). On the other hand, lower sensitivity earphones require more power and are a more durable option as compared to higher sensitivity ones as they don't damage the driver unit despite the amount of power they require. So lower sensitivity headphones should be paired with high power supplying devices to get good output sound quality.