When you rub your fingertips along a blanket you are exchanging charged particles like electrons and in some cases molecules missing an electron. This is due to friction. If you notice your fingers will actually become very hot if you do this over and over.
These electrons are negatively charged and create what we call an electric field around them which attracts positive charge and repels negative charge.
Atoms are typically neutral meaning that they have equal numbers of positive and negative charges and so aren't attracted or repelled very much by the electrons you have built up on your fingers. The charge you have built up on your finger all combine to create a strong electric field close by but not enough to pull other electrons away from neutral atoms. So then how does the build up of charge create light?
Well, there are freely floating electrons and ions in the air due to cosmic rays and radio activity in the Earth ionizing the air. These particles can be accelerated to very high energies near a build up of charge like that on your finger. Your charged finger then pulls these free electrons in the air toward it and on there way they collide with atoms in the air. These collisions excite the atoms which then emit light to settle back down to a lower energy state. That is why sparks create light.