Does that Mean I play out the chords in arpeggios?
Do I do it in quarter notes?

Got it from here http://cbda.org/hs/jazz/Bass_Jazz_Etudes.pdf

Apparently they want me to improvise.

Does that Mean I play out the chords in arpeggios?
Do I do it in quarter notes?

Got it from here http://cbda.org/hs/jazz/Bass_Jazz_Etudes.pdf

It means that you play walking bass. Some arpeggios, some scale tones, some chromatic approach notes. Yes, the walk 4 means walk in 4/4 time so it would mostly be quarter notes.

Apparently they want me to improvise.

Yep, but there are ways that are better than others. Start practicing with quarter notes, making arpeggios, but try to lead from one chord to the other. In a sense, don't just play mindless ascending arpeggios. ;)

Try also adding passing tones: ie, a C to F progression might have you playing C, E, G, F# on the way to F... F# isn't necessarily in the scale but it's a nice way to transition down to F.

Sometimes, instead of playing straight quarter notes, you can add the odd 8th note, although it can help to swing it a little bit to fit the feel of the song (shuffle style: instead of playing 2 eighth notes, you're essentially playing a dotted eighth and a 16th during that span).

Hard to explain, but it's really all about being creative and suiting the song.

walking alows you many freedoms, but you gotta be resposible. When it says walk your primary job is to keep the chord progression moving. There are many ways of acomplishing this and its all up to you

starting out with quarter notes is good advice. Once you get bored with that you can start changing it up with differents aproaches, inversions, times, etc..

Ah thats nice I'm going to try this out. Thanks you guys!

Ed Friedland's book "Building Walking Basslines" is great for this. Pick it up if you can.

Ed Friedland's book "Building Walking Basslines" is great for this. Pick it up if you can.
+1, and listen to Ray Brown (most notably played with Oscar Peterson).