These names might sound strange, but they reflect the position of the note in the scale.
The tonic is the main tone of the scale; the scale takes its name from this note.
The supertonic is just above the tonic, i.e. the second note of the scale (super here means 'over' or 'above').
The dominant is five notes above the tonic. The subdominant is five notes below the tonic (sub here means 'below').
The mediant is the midpoint between the tonic and the dominant, and the submediant is the midpoint between the tonic and the subdominant.
The leading note pushes up or leads back to the tonic.