It means to try to do something to the very best of your ability.It can be physical - for example run as fast as you can , until you cannot run any faster: climb a mountain which will demand the very most of your stamina and skill that you can use.. Or psychological - e.g. put the most you possibly can into your studies. As regards whether it's a good thing to push yourself - try it and see what happens. All I would say is don't do it in too many areas of your life at the same time. Sometimes I have found that if I push myself to the limit my capacities and skills increase. Othe times it has been too much. But hey - if you don't try you won't know where your limits are.