Couple of situations where it's potentially useful:
When your teammate is right behind you, asking him to defend his position can fend off faster cars from your rear end for a while.
If you're doing badly in a race, asking your teammate to push might be your team's only chance of picking up useful points.
The two most extreme settings (defend and attack, or whatever they're actually called) can have the biggest effect, but are also more likely to result in your teammate spinning or crashing out.
Sadly, although this is a fairly unique idea for a racing game, it doesn't tend to work all that well. Your team-mates in the game are usually so bad that, left to their own devices, they'll normally finish last or not far off it. If they were usually closer in ability to yourself, it could be a much more interesting feature.