What does this quote means by Thoreau: "However mean your life is, meet it and live it; do not shun it and call it hard names."How can I explain it...

Well that is a great quote.  Thoreau was an incredible thinking.  Here is an interesting picture of the guy, by the way.

To better understand the quote, make sure you have a good knowledge of all the terms being used in it.  Most are easy, but a few could use explanation:

mean life: a hard, unpleasant life filled with challenges and obstacles.

meet it: do not run away from it.

shun: to not look at, to turn away from, to refuse to acknowledge.

hard names: insults (and curse words!)

So, in this context, take a look at the quote: "However hard or unpleasant your life is, do not run away from it; do not turn away from it or call it mean names."

This is a call to "rise up to the challenges." It is very easy to give into discouraging thoughts and events in life.  It is very easy to just sit there and say "my life blows" and "why does everything bad always happen to me?"  But that doesn't get you anywhere.  The only course of action is to meet the obstacles head-on and overcome them.

For example, think about a man whose wife leaves him for a younger, more studly fella.  He could very well sit back, get fat, and complain to anyone who will listen that about how his life has been ruined and how much it sucks.  It could be an excuse to let his life run down...instead, it would make more sense to meet the challenge head on.  Improve, reflect, and move on.  That is a far more effective strategy.