The substance is, as has been said thermal compound (sometimes called TIM or Thermal Interface Material). It is there to improve the contact and heat transfer between the chip and the cooler. It should never be reused and never, ever ignored.
To remove it use a paper kitchen towel moistened with a suitable solvent, most computer stores sell cleaning fluid for this purpose.
Just wipe the heatsink clean, then use another, clean moist towel to carefully wipe the goo off the chip, try to work inwards to prevent excess material from getting onto the tiny electrical components that surround it. If some does spill over, get the towel a little wet and dab it onto the spillage, you'll never get it all off, these materials usually contain tiny metal particles so expect there to be a stain left behind. Allow the card to dry for a few minuets before applying fresh TIM.
It's a good idea to use a decent quality material, Arctic Silver is highly regarded but not every store carries it.
There is several ways to put the TIM on: I place a drop about the size of a grain of rice on the heatsink and spread it out to form a fairly even layer with a finger, you should see where the heatsink makes contact with the chip, it will be a brighter square where the metal has not oxidised.
Be EXTREMELY careful when reassembling the card, replacement screws are hard to source.
The 'X' shaped brace on the back should be tightened a turn at a time in a diagonal sequence and use a good quality, close fitting screwdriver.
I am not a nerd.