Melodic sequence on the lines "Send her victorious," and "Happy and glorious," from "God Save the Queen".
A sequence is taking a theme or passage, playing it, then more or less repeating it at higher or lower pitch. An example is found in Beethoven's Fifth Symphony. The first four notes are the theme. Beethoven creates a sequence by then moving the theme down. After that, he continues the sequence by moving it up and playing it three times.
A melodic sequence is one that only involves repetition only of the melody. A harmonic sequence involves repetition of a series of chords. If the quality of the intervals between the notes of the melody is to some extent altered (a major interval becoming a minor one and so forth, as is practically inevitable if the key is unchanged) we have a tonal sequence. If there is no such variation in the intervals (usually achieved by altering not merely the pitch of the notes but also the key) we have a real sequence. If there are several repetitions, some of them tonal and some real, we have a mixed sequence.