Romans 11

In Bible times, it was very common to graft olive trees. A branch from a good olive tree was taken and grafted onto a wild olive tree. The wild olive tree, called agrielaios, did not produce very good fruit. But the good cultivated olive tree, called kallielaios, did produce very good fruit. Wild olive trees would grow up and take up space with it's root system. To keep from having to cut down a tree and plant a new seedling, a branch from the good tree would be grafted onto the wild tree. This good branch would then produce fruit while getting nourishment from the wild tree root system. Several branches would be grafted onto a wild tree.

In Romans 11:17 we read, "But if some of the branches were broken off, and you, being a wild olive, were grafted in among them and became partaker with them of the rich root of the olive tree..."

God was using the grafting process to make a very important point. Instead of grafting a good branch onto a bad tree, God took a bad branch and grafted it onto a good tree. This was opposite of the way the first century people grafted olive trees. God had a good tree with a good root system. The Israelite nation was the tree with the root system of the patriarchal law, mosaical law, and the new law. The Gentiles were represented by the wild olive tree. God took the wild olive tree, the Gentiles, and grafted them into the good tree and it's root system.
The reference to the branches being broken off means that Jews who did not accept Christ were unacceptable to God. They were cut from the tree. This shows that just because someone has a sincere heart and believes in God does not mean that person will be acceptable to God. A person must believe in and obey Jesus Christ to be acceptable to God.

Only God has the power to graft a wild tree branch onto a good tree and have that branch produce good fruit. I am glad that God is a loving God and wants all men to be saved. I am glad he gave us the Bible so that we can know how to serve Him.
...Taken off the web.

I just wanted to add that in v. 23 it says, "...if they do not continue in their unbelief, will be grafted in, for God is able to graft them in again."
There is always a chance to change your mind and come to Christ.