A side channel attack is an attack that deduces secret information from environmental observations such as timing or power consumption.
A side channel of system is a way in which the system reveals information indirectly. Side channel attacks attacks can allow attackers to obtain confidential information even when the stored or transmitted message itself is not leaked.
A common class of side channels is timing timing-attack, where the duration of certain operations reveals information about the data that is being processed. For example, the number of elementary operations in an encryption algorithm may depend on the value of the key; the interval between network packets may be indicative of how much computation was required to generate the packet and thus of the content of the packet.
Other types of side channels include power consumption, electromagnetic radiation, noise, etc.
For questions about side channel attacks on cryptographic algorithms specifically, see also side-channel-attacks on our sister site about cryptography.