HMO - Health Maintenance Organization
HMOs tend to have the lowest monthly premium, but they require referrals to see specialists from a primary care physician (PCP). There is no out-of-network coverage on this type of network.
PPO - Preferred Provider Organization
With a PPO network, you can choose any doctor on their preferred list of providers, no referrals are needed. You can also use an out-of-network provider (ie., not on the preferred list), but you will have to pay more out of pocket.  PPO networks are the broadest and most flexible, but will increase your monthly premium.
EPO - Exclusive Provider Organization
With an EPO, you must pick from the providers on the list, or the insurance company will not pay. An EPO is like a PPO, but without out-of-network benefits. You do not need to choose a PCP or get referrals.
POS - Point of Service plan
A POS plan is like a HMO, but in some cases you can get out-of-network coverage like with a PPO. Typically you are required to get referrals, with some exceptions (eg., Humana).
For more information, see this article.