Within the command, the operator defines the action to be taken, which generally involved changing of deleting text in some way. Here is a quick summary of the available operators:

cchange operator
ddelete operator
yyank operator
~swap case (if `tildeop` is set)
g~swap case
guchange to lowercase
gUchange to uppercase
!filter through an external program
=filter through 'equalprg' or C-indenting if empty
gqtext formatting
gwtext formatting with no cursor movement
g?ROT13 encoding
>shift text right
<shift text left
zfdefine a fold

Some operators are so commonly used that Vim allows an entire command to be comprised of just the operator. When an operator is repeated twice, then that operation is performed over the current line of text. Here are few common examples:

yyYank the current line
ccDelete the current line then enter INSERT mode
ddDelete the current line