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Odometry is/can be used in multiple components in the navigation stack. Costmaps might be defined in the odometry frame and thus transformed by odometry. The controller can used odometry to determine the next command (this depends on the implementation/algorithm).
Usually odometry is send in two ways: TF + odom message. TF nicely embeds with all other tf frames, while the message contains additional uncertainty information.
AMCL uses odometry as an essential input.