Computer A sends a SYN packet to establish the connection. The SYN stands for synchronize (and refers to sequence numbers).
Computer B receives the SYN packet, and sends a SYN/ACK back to A: Syn to synchronize, and ACK to acknowledge the receiving of A's SYN packet.
Computer A receives this SYN/ACK, and sends an ACK back to B to acknowledge the receiving of B's SYN/ACK packet. At that point, the connection is said to be open. So yes, the second ACK is just an ack of an ack.