What does study to shew thyself approved unto God mean?

Contrary to much of modern professing Christian teaching... the Bible speaks of the "Last Day" of God's plan. A future time in which all men will give account of themselves to Him, regarding the "works" they've done in their lives. Whether or not those works "measure up to" WHAT THE BIBLE SAYS; the way God commands that His Children should be [i.e. see - Matthew chapters 5-7].

"...behold, I come quickly; and My reward is with Me, to give every man according as his work shall be." (Rev.22:12)

This future event is better known as "Judgment Day."

Most modern religions teach that all men are judged and sentenced immediately at death, and live on in some other place or existence, thus negating the need for the Bible's prophecies of the "Last Great Day."

Yet, even God's saints [those He's been calling and sanctifying unto Himself since 'Abel'] will be "assessed" by Jesus when He returns, to see what they did with the blessings He gave to them; whether or not they conducted themselves worthy of their Master. A number of His parables reveal this time of "Judgment":

"...unto one He gave five talents, to another two, and to another one; to every man according to his several ability; and straightway took His journey [Jesus went to heaven]...

"After a long time the Lord of those servants COMETH [Jesus returns to earth], and RECKONETH WITH THEM... (Matt.25:15-19).

Jesus is coming back... among other reasons... to reward those who have been called during this time of the Firstfruits, according to whether or not they, as branches on God's Vine, produced "good fruit" during His absence... and qualify to co-rule the Kingdom of God with Him.

II Timothy 2:15... is making reference to the behavior of God's elect during Jesus' 'physical' absence from earth, in the light of this future assessment. Conducting themselves in a manner that is "worthy" of their Master... and worthy of the reward for which they strive.

"You then, my son, be strong in the Grace that is in Christ Jesus... Endure hardship with us like a good soldier of Christ Jesus. No one serving as a soldier gets involved in civilian affairs -- he wants to please his Commanding Officer.

"Similarly, if anyone competes as an athlete, he does not receive the victor's crown unless he competes according to the rules.

"The hardworking farmer should be the first to receive a share of his crops.

"Reflect on what I'm saying, for the Lord will give you insight into all this...

"Here is a trustworthy saying: If we died with Him, we will also Live with Him; if we endure, we will also reign with Him. If we disown Him, He will also disown us; if we are faithless, He will remain faithful, for He cannot disown Himself.

"Keep reminding them of these things. Warn them before God against quarreling about words; it is of no value, and only ruins those who listen.

"DO YOUR BEST TO PRESENT YOURSELF TO GOD AS ONE APPROVED, a workman who does not need to be ashamed and who correctly handles the Word of Truth." (II Tim.2:1-15 NIV)

If you are Christ's... you will be among the first of all mankind to be rewarded first upon His return [from His long journey]. When that time comes, all of His servants will give account of themselves to Him, as His parables reveal.

Of some of them, He is proud, and rewards with great authority in the Kingdom over the nations:

"'Well done, My good servant,' his Master replied. 'Because you have been trustworthy in a very small matter, take charge of ten cities.' (Luke 19:17 NIV)

This servant of God "presented himself approved of God" when his time of reward came.

While others won't fare so well.

"...I will judge you by your own words, you wicked servant! You knew, did you, that I am a hard man, taking out what I did not put in, and reaping what I did not sow? [this servant didn't show himself 'approved of God'] ...those enemies of Mine who did not want Me to be King over them -- bring them here and kill them in front of Me." [verses 22-27]

"Judgment Day" [the Last Great Day] is coming upon all men. And God's saints will be Judged and Rewarded first.

"For it is time for Judgment to begin with the Family of God; and if it begins with us, what will the outcome be for those who do not obey the gospel of God?" (I Peter 4:17 NIV)

II Timothy 2:15 means: 'Conduct youself according to the Word of God in Humility, Truth and Honesty. Fear God and keep His Commandments. For He expects this of all of His Children. [Eccle.12:13-14]

God's servants should be "doing their best" [on their best behavior] trying to "please their Master" [their Commanding Officer] on behalf of others in Jesus' name. God "approves" of this.