Galatians 4:1 & 2

"What I am saying is that as long as the heir is a child, he is no different from a slave, although he owns the whole estate. He is subject to guardians and trustees until the time set by his father." NIV translation

In chapter three, we saw how we, as Christians, were all made to be sons of God through faith in Jesus Christ. This passage is talking about the period of time in a child's life before they are mature and considered to be legally of age. Today, in the USA, that is determined in many cases by the law such as legal drinking age, drivers license, etc. 

During Paul's time, it was not up to the government or a law but the father of the child. Until the father decided that the son was mature enough, he was considered to be a child and, though he was a legal heir, he did not have control of anything to do with the estate. The child was still, in effect, a slave to the guardian or trustee that was put in charge of them.

Galatians 4:3

"So also, when we were children, we were in slavery under the basic principles of the world." NIV translation

Paul is talking about his Jewish heritage and the fact that he was a slave to the law.

Galatians 4:4 & 5

"But when the time had fully come, God sent his Son, born of a woman, born under law, to redeem those under law, that we might receive the full rights of sons." NIV translation

Freedom from the law only comes through faith in Jesus Christ. Through Him, we all are given the "full rights of sons".

Galatians 4:6 & 7

"Because you are sons, God sent the Spirit of his Son into our hearts, the Spirit who calls out, 'Abba, Father.' So you are no longer a slave, but a son; and since you are a son, God has made you also an heir." NIV translation

If we have accepted Jesus Christ as our Lord and Savior, then, the Holy Spirit lives in us and testifies that we are sons of God. Because we are sons, we also are heirs meaning we inherit all that is God's (which is everything).