I'm a student and I'm working on a low power communication project. I am trying to design a PCB using the TI CC2540 sample design. There is a MC-306 (32.768kHz, 12.5pf, and 20/50ppm). 

I don't know what the 20/50ppm rating is. For me, the size is very important, so I decided to replace it with the FX135A, but its ppm is -20/+20. Will it cause a problem if I use this one instead?

What is the ppm rating in the crystal oscillator?

Like Olin said, ppm stands for parts per million, and it indicates how much your crystal's frequency may deviate from the nominal value. The MC-306 exists in a 20 ppm and a 50 ppm version. For the 20 ppm version this means that the frequency will be between 32.7673 kHz (32.768 - 20 ppm, or x 0.999980) and 32.7687 kHz (32.768 + 20 ppm, or x 1.000020). These numbers may give you a comfortable feeling, but remember that a month is 2.6 million seconds, so if you want to use a 20 ppm crystal to build an alarm clock, it may have an error of 1 minute per month.
Crystals are available is different precisions, +/-20 ppm is more or less standard, for 10 ppm you'll pay more.
Also, this is basic precision. This frequency may deviate depending on environment factors, mainly temperature.