The easiest explanation of 'truncation error' is to try to imagine what would happen if you tried to write down the decimal value of Pi. At some point, you would get bored, or you would die, at which point you would cease writing. This is where the truncation error occurs. The fact that you've stopped writing (i.e. truncated the result) means that your answer to the value of Pi is now inexact.

That's all.
'Truncation error' sounds a bit nasty, but it just refers to the error introduced when you stop calculating a value. This sort of thing pops up in numerical methods when you try to determine the value of Pi, or e raised to a power and so on.

Usually you only need to determine the truncation error to the point where the truncation error is smaller than other errors, such as errors introduced by limitations of floating point numbers.