Many origins of decorated eggs can be found in eastern and Central European cultures, including the Ukrainian tradition where decorated eggs, called psyansky, pre-date Christian traditions.
Decorating eggs for Easter began when Orthodox Christians were looking for a way to preserve eggs while fasting during the tradition of Lent, which is observed for 40 days in the time period approximately leading up to Easter. One way to keep them from going to waste was to boil the eggs and keep them until the fasting period was over. The boiled eggs were decorated before serving in celebration of breaking the fast. Christians and many others continue the tradition of decorating the eggs even if they are not observing Lent.
The Easter Bunny is a symbol used in folk lore that shows a rabbit with a basket of decorated eggs, candy (like chocolate) and sometimes toys. These goodies were traditionally given to children. There are similarities between the Easter Bunny and Santa Claus in traditional stories as they both bring gifts and are symbols of cheer. According to German origin stories, the "Easter Hare" also judged whether children were good or bad at the start of the Easter festival season.
Whatever your traditions, we all wish you a very Merry - oops! - Happy Easter!