In most instances, whenever two devices want to communicate, they use the TCP protocol to ensure the message reaches both devices. The first process is known as the TCP three-way handshake. Once the handshake is completed, then data is allowed to flow between both devices. In a TCP SYN flood attack, the attacker sends a constant stream of SYN packets to the victim:

On the victim's end, for every SYN packet received, it must reply with an SYN/ACK packet. The attacker would receive this SYN/ACK packet but would not respond to it, therefore creating a lot of half-open connections on the victim machine. Remember, the attacker is continuously sending TCP SYN packets, which would eventually cause the victim's machine to exhaust its resources and not be able to create any future connections with other devices as long as the attack continues.