minimum detectable signal of an IMU (MPU 6050)
THe MPU6050 has 16-bit converters on it, that means it knows how to count from 0 to 65535 (or -32768 to 32767 depending on if 2s complement is used). Any reading you receive from the converter will be some number from 0-65535 (or -32768 to 32767) and you will have to convert that number in to a meaningful °/s value. 

In this particular case, if you use the +-250°/s range, the device is able to measure any rotational velocity from -250°/s to 250°/s which means it has a dynamic range 500°/s. 

If you divide the dynamic range (500°/s) by the converter dynamic range (65535), you get a measurement which tells you how much each count is worth in °/s. In this case: \$\frac{500°/s}{65535LSB}=0.0076\frac{°/s}{LSB}\$. 

This is exactly what the "Scale factor/sensitivity" tells you \$\frac{1°/s}{131LSB}=0.0076\frac{°/s}{LSB}\$. It means that every time the device reads back 1LSB more than before, it's spinning 0.0076°/s faster.

So, to use this sensor, assuming it goes from 0-65535, you will do the following math: \$(reading-32768)*0.0076\$. Likewise, if the device uses -32768 - 32767, you'll do the following: \$reading*0.0076\$

Hope this helps.