I see that Monero's software allows me to mine on my home computer. What is a mining pool and how is it different from just mining on my own?
A mining pool spreads the risk/reward of hitting a block, so you'll get more consistent results--though you'll likely pay an administration fee.
Think of it in terms of a lottery pool. If every week you put in $10 and the total is $100 in your lottery pool, you'll get 10% of the winning payout--minus any administration fees. Whereas if you buy $10 of tickets by yourself, your odds of winning go down, but you receive 100% of the reward and pay no administration fee.