Fan headers are connection points on the motherboard that cooling fans can be connected to. Fans can also be connected straight to the power supply, but when connected to the motherboard you gain much finer control over them through software.
SATA is an interface used to connect mass storage devices such as hard drives and Blu-ray drives. SATA 3 has a native transfer rate of 6 Gbit/s, which is twice as fast as SATA 2, the previous revision. This is particularly useful if you use an SSD as it can perform at higher speeds.
Devices with a HDMI or mini HDMI port can transfer high definition video and audio to a display.
More USB 3.0 ports allow you to connect more devices to your computer that support USB 3.0. USB 3.0 is an improved version of USB 2.0 which offers faster transfer rates.
The motherboard has USB 3.0 headers, which are pin connections that you can connect additional USB ports to.
RJ-45 ports are used for LAN (Local Area Network) connections. With more ports you can achieve increased bandwidth across a LAN, or connect to multiple networks. It also has the added benefit of not losing connection to the network if one fails.