People who work out with a training partner tend to stick with their workout routines more than people without one. They provide accountability and motivation.
So what should you look for in a training partner?
For one, make sure they are reliable. After all, a training partner doesn't do you any good if they are constantly bailing on workouts. If you both will be in the same physical location for the workout, make sure they won't consistently be late.
Find someone who has similar goals to you. It doesn't make much sense to have a partner who is training for a marathon when you're training for a power-lifting meet.
Make sure you are compatible with one another. Someone who just grates on your nerves is going to bring negativity to your workouts and could impact your performance.
Your training partner should at least be at the same level of fitness as you are. Note that I said "at least". Studies have actually shown that finding a partner whom you perceive to be more advanced, harder working, etc. will push you even further.
If your schedule is unpredictable, or you don't know anyone at your gym to partner up with, a virtual partner can be just as effective. Maybe you have a friend across the country, or maybe you're part of an online fitness community related to your interests. It's not difficult to find someone out in cyber land to pair up with!