In the TCP/IP protocol, a three-way handshake takes place as a connection to a service is established. First, in a SYN packet from the client, to which the service responds with a SYNACK. Finally, the client responds to the SYNACK and the connection is considered established.
A SYN Flood attack is when the client does not responsd to the service's SYNACK and continues to send SYN packets, tying up the service until the handshake times out. The source address of the client is forged to a non-existant host, and as long as the SYN packets are sent faster than the timeout rate of the service host's TCP stack, the service will be unable to establish new connections.
source: nmrc - Syn flood attack