It means there is a power supply issue - the coloured square (cryptic in some belief that rendering anything understandable would consume additional power) is described here: https://www.raspberrypi.org/forums/viewtopic.php?f=29&t=82373
The solution is to try a different smartphone power supply, or a different USB cable, or both.
is that the same gradient square he is talking about? it sounds like he means the coloured square that appears at POST stage. i've not heard of this undervoltage signal or seen it but i think that appears during normal operation and is overlaid on the command line/gui when the input voltage drops below 4.65V. or maybe that big square does mean undervoltage and i've misunderstood all this time!
I'm not sure about the stage it appears at, or if it persists for during the linux boot process, but I had thought it was overlaid by the GPU with some code
perhaps with no interaction with the OS so could appear at any time the supply dips. No idea though, I could be totally wrong.
Raspberrypi.org are not famous for good documentation - they expect it to be crowd sourced, but they have no better way than that poor forum
thread (108 posts to read through to understand bits of this feature, and no images of it) as far as I can tell.
It sounds like a power issue. If you have an appropriate meter you might test the output of your micro USB power cable before plugging in the pi although i imagine that is okay since it turns on. I find that some wired keyboard/mice require an external power supply (e.g. powered USB hub) but i pretty much exclusively use a wireless radio receiver with wireless mouse keyboard as it requires less power from the pi (batteries in mouse and keyboard).
If possible try a different keyboard/mouse and use only one at a time.