Question

This is might come under literature, but anyway,
"If you can force your heart and nerve and sinew
To serve your turn long after they are gone......"
-'If' by Rudyard Kipling. What did he mean by that?

Answer 1

And the lines that come a little after that -
" If you can talk with crowds and keep your virtue,
or walk with Kings - or lose the common touch. '

Answer 2

Keep in mind that this poem was written to his son and that it is a list of virtues he wishes his son to gain as he matures. Also the following two lines give us a clue as to what he is talking about:

If you can force your heart and nerve and sinew
To serve your turn long after they are gone,
And so hold on when there is nothing in you
Except the Will which says to them: "Hold on!"

He is saying "Never give up". Even when everything in you dies will yourself to continue on.

The other two lines you reference are easier to understand if you put them in to context using the last two lines of the stanza:

If you can talk with crowds and keep your virtue,
Or walk with Kings---nor lose the common touch,
...
Yours is the Earth and everything that's in it,
And---which is more---you'll be a Man, my son!

He is saying to his son that if he can keep his virtue by not giving in to peer or societal pressures, even if he becomes famous, that there is nothing he cannot accomplish.

That's my interpretation anyway. I'm always open to other insights.