Kaluza-Klein particles are 4-dimensional particles with a higher dimensional origin. Kaluza-Klein modes (modes refers to their quantized momenta) are distinguished by their extra dimensional momenta.
They travel in the extra dimensions, yet, leave traces of their existence here in the familiar three dimensions. They would be fingerprints of higher dimensions in our three-dimensional world.
They have momentum along the extra dimensions, that is, directed perpendicular to the usual dimensions.
They are additional ingredients to an extra dimensional universe. They are the 4-dimensional imprint of a higher dimensional world. Should these Kaluza-Klein particles exist, and be sufficiently light, high energy collider experiments should produce them, and they should be found in the data. If we could measure and study their properties, they would tell us everything there is to know about higher dimensional space. They are particles, like the familiar particles we know, however, carry higher dimensional momenta. The Kaluza-Klein particle's mass is determined by the higher dimensional geometry. However, their charges are the same as known 4-dimensional particles.