In Chapter 15 of "To Kill a Mockingbird", how do Scout and Jem save Atticus?

In Chapter 15, a group of town men come to the jail in a mob.  Their plan is to go inside, get Tom Robinson, and lynch him.  Atticus is the only one who stands in their way.  At first, it doesn't look good.  The mob is fired up and ready to attack.

However, the kids - Scout, Jem and Dill - step in.  They have gone to the courthouse against orders, and fearing for Atticus, they step out into the crowd.  This surprises the men, but it isn't until Scout mentions Mr. Cunningham by name, and tries to remind him that she goes to school with Walter, that the spell of the mob is broken and they leave.

This scene is intended to show not only the nature of the community, but also the nature of a mob mentality.  People in a group can't always think for themselves.  Individually, most of these men are good men - as a group, however, they are swayed by social attitudes and standards, such as racism.  This is proven by the jury's vote.  Atticus acknowledges that the jury knows that Tom is innocent - but because of social attitudes and tradition, they can't vote against the word of a white man (Bob Ewell).