WAP means HTTP connection, which has to "pull" data from server from time to time due to its Request-Response mechanism. The traffic is wasted during the polling. Besides, the connection must go through operator's WAP Proxy, which may cause connection problems sometimes. This mode only benefits users with unlimited WAP data plans.
Internet means continuous connection, no polling. Data will be pushed from server. The traffic is optimal compared to WAP. This mode is actually recommended for all users.
To choose between WAP and Internet, you need to configure the APN of your phone. If you do not know which is which, one hint is to look at the "Proxy" or "Gateway" part of the settings. Internet connection normally does NOT have "Proxy" or "Gateway" set.