Reading the instructions could be a good start.
Anyway, they're space-saver connections for video and audio by the look of it. The one with the 3x RCA/phono sockets is stereo audio (red for Right chand the white for Left ch), and the green with a yellow band is for composite video or the Y part of component video. The selection is made via the TV's input menu.
The one with the blue and the red RCA phono sockets is for the remaining parts of the component signal: R-Y and B-Y.
Composite (yellow - video) + stereo audio (red + white) is easy to understand. You'll get this as the basic audio and video output from most video devices such as cameras, camcorders, VCRs (via a SCART cable or adapter, usually), basic games consoles (e.g. Nintendo Wii), basic DVD players, video senders, some satellite receivers, etc etc.
Component video (Y, R-Y, B-Y) + stereo audio is a higher quality video signal with basic stereo sound. The Component element is because the video signal is split in a way that makes it much better quality than simple composite video. It also allows the connection to carry something better resolution than just standard definition video.
Component was a popular choice of DVD players in the era before Blu-ray and its digital HDMI connection for picture and sound.
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