It's a normal thing, all it means is that it's re-starting. If you hadn't restart it yourself, it might be responding to a glitch also a lot of other reasons but it's usual.
It basically means the box is re-booting, if its a Scientific Atlanta box that is. If it says HAL2 boot or a spinning circle after that, no prob but if it shows four dashes and it's not a 8000 or if it is and shows for more than a few minutes, call the cable company because that means unauthorized or some kind of failure.
When the cable box says "boot", it means that the cable box is booting/re-booting. Don't do anything yet, wait until the display goes blank, then in a couple of minutes, the time will appear.
If by converter box you mean a digital converter box, the type that are being subsidized by the government, you don't. If you mean a tuner box, it is because the cable line is transmitting data, and it has to be interpreted into a video signal your TV can use.
A LAN is a "Local Area Network". Your cable box is providing one or more Ethernet ports by means of which you can access the Internet.
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A cable box is a device attached to a set top box connecting a house to a cable service.
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Weak signal
Not if it is THEIR cable box. You pay to use the box. No pay, no box.
Donald Walter Kirk invented the cable box.
You can select the cable length in the option box.
Sometimes a cable box malfunctions because of a power surge that consequently fries the box, unfortunately. Other times the cable box is not compatible with the TV.