To average up means buying on a rising market, so as to lower the overall cost.
For example: Investor A buys XYZ at $20 per share, and as the stock rises he buys equal amounts at $25, $28 and $30 per share. This would bring his average purchase price to $25.75 per share (20 + 25 + 28 + 30)/4 = 25.75.