Egg rolling, or an Easter egg roll
is a traditional game played with eggs at Easter. The versions of this game vary from one country to another, and they are traditionnally played with hard-boiled decorated eggs.
Here's a photo of the White House Egg Rolling...
... in 1929 ! (1)
Click on the White^^ House in the background :
you'll get more details on the egg roll tradition.
By the way, an "egg roll" or a "pancake roll" is the Americans name of a "spring roll" : it is "a savoury Chinese pancake which is rolled up, filled with small pieces of vegetables and sometimes meat and fried" (from the Cambridge Advanced Learner's Dictionary online )
(1) Picture from the Public Domain