If the sniffer has all the packets that you sent, he can reconstruct all the data (files, mails, whatever) that you sent, for the simple reason that he has everything that the intended recipient has. If the sniffer only has some of packets, then he can still reconstruct part of your traffic — files with holes, so to speak. For example, if he has only some of the packets you received from an HTTP server, he has pieces of the file, knows in what order to put them, and has a rough idea of how much he's missed, because each TCP packet contains a sequence number that's incremented by 1 for each successive packet, and TCP packets have different sizes but often with not a lot of variance.
If the connection is encrypted (e.g. because it uses SSL), the sniffer only sees the ciphertext. So he knows who you're communicating with, and how much data you're exchanging (except for rare protocols that keep the target of packets confidential from eavesdroppers, but that makes routing difficult so is not done often).
If you have working encryption on a wireless network, then an eavesdropper who doesn't have access to the network (i.e. doesn't have the wifi password or whatever authentication is required) might still know how much traffic you're exchanging but not with whom. So there is some gain in using wifi encryption even if you're encrypting at the application level anyway. Another benefit of wifi encryption is that it doesn't leak non-encrypted data such as DNS requests, which can reveal more information about your network than you care for an eavesdropper to obtain without effort. Another benefit of wifi encryption is that someone might want to route traffic from your network, either to leech your bandwidth or to commit illegal acts that would be traced back to you. A third benefit is that if you've accidentally left some application unsecured on your local network, the wifi encryption will protect that application from an external attacker with no physical access to plug in his own device.
In summary, wifi encryption does provide significant protection against external threats. Note that I wrote “working wifi encryption” above: WEP is famously broken (takes just a few minutes to crack), WPA2 is fine against external attackers. WEP and WPA(2) are supposed to also provide protection against insiders, but that aspect is broken: under WPA2-PSK, the most common variant (with a single shared secret key), any participant can effectively eavesdrop and spoof other participants (see Any advantage to securing WiFi with a PSK, other than to keep out unauthorized and other wpa2 questions).
