I'll follow suit Boyd. Other than to post the reply to address your question, I won't post any other discussion on this particular topic.
What do I think Jesus did for mankind?
Jesus' life, death and resurrection was the ultimate rescue plan. The word Salvation translates directly to "Rescue". When we read "... you have been saved" or "... you will be saved". It is the equivalant of "... you have been rescued".
From nearly the start of the world, the 3rd chapter of Genesis until today, the world has a need of being rescued from itself. Christ's purpose was to rescue that world and restore the order of the Garden, culminating sometime in the future, in that restoration.
What are some of my basis for this belief?
The Old Testament is filled with "types and shadows". The ark is one of those types. The purpose of the ark was to rescue Noah and as many as would come with him from the impending flood. That salvation helped to cleanse the world from the sin it was caught in. It didn't eliminate the sin, however.
Next, Israel was chosen by God to be a light to the people around it.
Deut 4:5-8 reads:
“Look, I now teach you these decrees and regulations just as the Lord my God commanded me, so that you may obey them in the land you are about to enter and occupy. Obey them completely, and you will display your wisdom and intelligence among the surrounding nations. When they hear all these decrees, they will exclaim, ‘How wise and prudent are the people of this great nation!’ For what great nation has a god as near to them as the Lord our God is near to us whenever we call on him? And what great nation has decrees and regulations as righteous and fair as this body of instructions that I am giving you today?
As a result, Israel was to point the peoples around it to God. As you can see by reading the Old Testament, that didn't work out so well. God was able to keep
his promise to David, however, and bring a King into the world that would reign forever. That King was Jesus who's purpose was to save us from our sins.
There has been a lot of debate here on who Jesus' death redeemed (there is a reference to the sin sacrifices in the law).
John 3:16 states that Christ loved the world, sent his son for that world so that all who believe in him are rescued.
Do all people receive that rescue? No, not all people believe in Jesus. Could all people be rescued? Absolutely.