I often watch stocks and dabble here and there for fun. One practice or pricing of stock I do not understand. Often stocks, which are being bought at the current ask price, will continue to lower the ask price. At the same time, they are raising the bid price. Why is this? Seems to me, they are trying to get investors to sell the stock... is this the case?

You're referring to the bid/ask spread. A smaller bid/ask spread usually is a good sign of efficiency and liquidity. The way it moves is basically supply and demand and you can get a good image of the supply and demand if you look at level 2 quotes. That's the way big board stocks operate, penny stocks are different though.