What is "rightly dividing the word of truth?"
Because the Bible is God's Word and is our only source of revelation from God, it is very important that we study it very diligently and properly. How we are to study is an important question because it does not affect just one area of doctrine. Rather, it affects our entire approach to God's Word. It determines how we will study. There is just one important verse in all of Scripture that tells us how to study. Since God is the author of our Bible, He should know how to study it.
2 Tim. 2:15 Study to show yourself approved to God, a workman that needs not to be ashamed, rightly dividing the word of truth. (UKJV)
"Rightly" comes from the Greek word "orthos" which means "in a straight manner."
"Divide" comes from the Greek word "orthotomeo" which means to dissect into separate pieces. Hence, to "rightly divide" -- means to cut straight, into separate pieces or parts." We are instructed by God to make straight cut divisions in His Word.
Since god has commanded to divide the word of truth, there must be divisions in the Bible for us to divide. Rightly dividing the word of truth is simply recognizing the divisions that God has placed in the Bible. These divisions are commonly called Dispensations and ages.
A dispensation is a way of dealing -- an economy. It is not a period of time. It is a method of God dealing with man. A dispensation is God's response to man's choices.
At this point, a few examples of how God can change the way He deals with man, and yet, not change anything about Himself would be helpful. Let us consider Adam and Eve before the fall:
Genesis 1:28 And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.
From this verse, we can see that God blessed Adam and Eve. Before man ever sinned, man was in a condition of being blessed by his Creator. But, what do the scriptures later record about Adam and Eve?:
Genesis 3:17-19 And unto Adam he said, Because thou hast hearkened unto the voice of thy wife, and hast eaten of the tree, of which I commanded thee, saying, Thou shalt not eat of it: cursed is the ground for thy sake; in sorrow shalt thou eat of it all the days of thy life;  Thorns also and thistles shall it bring forth to thee; and thou shalt eat the herb of the field;  In the sweat of thy face shalt thou eat bread, till thou return unto the ground; for out of it wast thou taken: for dust thou art, and unto dust shalt thou return.
This text shows us that God cursed the ground because of Adam and Eve's sin. God did not change. Adam and Eve changed. God would now have to deal differently with Adam and Eve because they (Adam and Eve) had changed. This is a dispensational change. This is "right division."
An age is a period of time dealing with things God has predetermined. The following chart will help you visualize how "right division" works.