I'm going to aim for simple and scientific here, though I will say melody is far more than I can write here or in any book.
There's a minor misunderstanding here, because Melody is the combination of line and rhythm. (and arguably harmony also)
The 3 concepts to concern yourself with in a Melody are Line, Rhythm and Harmony
Let's remove/ignore harmony to make it slightly simpler for now
Harmony is the underlying harmonic context of what is being played. In a simple C major chord, the Harmony is C major, but if you were to play C then E then G, you would also have an underlying C major harmony, even though the notes weren't played at the same time.
line is the pitch that each note is played at in relation to other notes.
It's important to consider where notes lie in relation to those around it because your ear picks up on the relative distance between notes. If you play a C and then a G, your ear picks up the perfect 5th and G sounds Consonant. If however you play a C# then a G then your ear picks up a diminished 5th, and the G sounds Dissonant. The second note never changed, but it's relation to the notes around it did.
How would you describe Rhythm
Rhythm is the time that a note is played in relation to the notes around it.
Discounting Accents, tempo and all the other stuff that is involved, rhythm at is simplest is the time that notes are played. Your ear is extremely sophisticated at picking up patterns, and for that reason we can recognise when a certain beat pattern is being played
How would you describe Melody
Melody is the combination of Rhythm and line to create a pattern of notes.
Please note that you are asking for a simple answer to a grossly wide scoped question that has reems of books written on the subject. For me to go beyond the technical definition would be committing to an answer I don't know myself yet!
Some other sites that might be of use:
Wiki on the Psychology of music
A few books on the psychology pf Music
Melody defined by Google
Leonard Bernstein on Melody