Airdecap-ng is a tool for decrypting WEP / WPA / WPA2 capture files. WEP/ WPA/ WPA2 are the different encryption algorithms provided by IEEE 802.11 suite of protocols.

From these encryption algorithms, WEP used RC4 stream cipher provided by RSA security. The small IV (Initialization Vector) lengths, weak IVs, direct use of master key in encryption are some of the main problems with WEP. WPA comes with two flavors, RADIUS and PSK. PSK is vulnerable to dictionary attacks.       

Airdecap-ng is very handy tool for verifying the WEP key or WPA pass-phrase which is acquired using one of the WEP or WPA cracking tools. (like aircrack-ng, airsnort etc).  It can be also used to strip the wireless header from the wi-fi captured files