Who is probably leaving them gifts?
I assume you're referring to the unusual gift items left in the knothole of a tree for Scout and Jem. The gifts were left there by Boo Radley. They consist of two pieces of chewing gum, a ball of twine, a broken pocket watch, two old "Indian head" pennies, a full pack of gum, a tarnished spelling bee medal, and a couple of figurines of Scout and Jem, intricately carved out of soap.
Boo is trying to communicate with Jem and Scout, his only real connection with the outside world. The gifts are important because they mark the point in the story when the attitude of the children towards Boo starts to change. Though understandably wary at first, they come to accept Boo's tokens of regard for the spirit in which they are given. Unfortunately, they are not able to post their little thank you note in the knothole as it has been filled in with cement by Nathan Radley, Boo's brother. He claims he only did it to cure the tree, as it is somewhat diseased. Whether that is true or not, Nathan has instantly shut down Boo's one meaningful connection to the outside world.