Not that you can't ask here, but given that you have a teacher and your teacher gave you the material, your teacher would be the perfect person to ask.

Anyway, let's start with a few very basic definitions:

• Scale: An ordered collection of notes. For our purposes we'll use a C Major scale which you are probably familiar with.
• Chord: Several notes played at the same time
• Arpeggio: The notes of a chord played one at a time in succession.

Now how do they relate to each other? There's a lot to this question so, again, we'll have to keep it very basic.

To start with the chords we use are usually built from a scale. If we take a C Major scale and harmonize it in 3rds, we'll get a chord for each degree in the scale. In other words we'll create a chord from each scale degree by stacking 3rds which is like taking every other note from the scale.

• CMaj7: C, E, G, B
• Dm7: D, F, A, C
• Em7: E, G, B, D
• FMaj7: F, A, C, E
• G7: G, B, D, F
• Am7: A, C, E, G
• Bm7(b5): B, D, F, A

So we used a scale to build some chords. And now we can use the chords to build a chord progression:

Dm7 | G7 | CMaj7

Now let's say the pianist is playing those as full chords (playing all the notes simultaneously). As a bass player your job is to outline that same harmony but usually using single notes. The easiest way to do that is by using arpeggios. So during the bar of Dm7, you'd play the notes D, F, A, or C. And during the bar of G7 you'd play the notes G, B, D, or F. These are all notes of C Major scale so you could just play that. But you'll outline the harmony better—and it will sound better—if you target the chord tones, or the notes that make up that specific chord, by playing an arpeggio.

Walking Bass

All that said, there's a bit more to walking bass lines that just playing arpeggios. You usually want to play certain notes on certain beats and throw in some passing notes as well. Here are few tips to get started:

• The first beat should usually be the root of the chord (D for Dm7). It pretty important that the bass player is covering the root of the chord because the pianist or guitarist playing the chords might not.
• The third beat (assuming the chord lasts a full bar) should be a chord tone
• The second and fourth beats may be passing tones (leading you from one chord tone to the next) from the chord scale. (Remember how we built the chord from a scale? We can use notes of that scale as passing notes—technically we'd probably say the "chord scale" is D Dorian for Dm7 and G Mixolydian for G7 but those are still the same notes as C Major)
• Don't leap into or away from any passing tone or non-chord tone. Try to use stepwise motion instead.
• Chromatic half-steps from above or below leading into the next chord can work well and are very idiomatic in jazz bass lines. Just don't abuse them too much or it starts to sound cliché.

That's definitely a simplification of it and those rules are not set in stone. But that should get you started.