Your friend is talking about harmonized chords and chord progressions.
You can get details at just about any self-respecting music instruction site (I myself have posted this stuff here many times).
In short, you harmonize a note of a scale by building a triad, with the note two notes higher in the scale, and the note four notes higher in the scale. So, for instance, the harmonized chord build on the second scale degree would have the second, fourth, and sixth of the scale. For example, the harmonized D chord in the key of C would have D, F and A.
These harmonized chords are referenced by their scale degree in roman numerals. In addition, the chord of a given scale degree in a major key will always have the same quality (major/minor), so most people will reference the minor chords using lowercase numerals.
So, for any major key, the harmonized chords are:
I-ii-iii-IV-V-vi-<vii>
For minor keys it's:
i-<ii>-III-iv-v-VI-VII
The vii chord of major and the ii chord of minor keys are special; because they span both of the half-step note jumps in the scale, the fifth of the chord is diminished in addition to the minor third, making those two triads diminished.
Apply this to the key of C major, and the natural chords are:
C-Dmin-Emin-F-G-Amin-Bdim
If you were in the key of C minor (same signature as Eb major), the natural chords would be:
Cmin-Ddim-Eb-Fmin-Gmin-Ab-Bb
Now, your friend is recommending you practice playing a bassline for a ii-V-I chord progression. That means the guitarists and keyboardists are generally going to start a verse or passage by playing the ii chord, so you need to play notes that are in that chord or work well with them. In the key of C, you want to construct a bassline around the notes D, F, and A. Then the chord players will change to V. In the key of C, you'll want to construct a bassline around G-B-D. Then the chord will change again to I. Again in C major, you want to build your line around C-E-G.
Now, in simplest terms, all you have to do is play the root. But if you're trying to learn a jazz or blues chart and construct a walking bassline, pumping the root is not going to sound very interesting, so you'll need to know the natural chord you're on, the notes in it, and in some cases the notes that can be added to the chord (2nd, 4th, 6th, dominant 7th or major 7th depending on the chord's quality and where you're going next) to make it sound like you're heading for the next chord (known as "resolving" to the next chord).
As far as "root-fifths", your friend may be talking about alternating root-fifth intervals as you move through the line (a common element of funk basslines), or he may be talking about double stops, where you fret your root note, then fret the fifth of that note on the next higher string and play both together. Or, he could be talking about "root-third-fifth" which is the principal walking line in 12-bar blues songs, or he might have simply been trying to further explain natural harmonization.
