Train like you race, race like you train. Have aerobars on your bike? Better try 'em out in training before you attempt to get down in them during a race. Doing a race that'll take you longer than 90 minutes? Be sure you practice your nutrition strategy--both in terms of what you eat and when you eat--sometime before the big day. Planning to wear a sombrero for the Cinco de Mayo Splash 'n' Dash? Okay, maybe you don't need to do your training runs around town in a sombrero. That might earn you some strange looks. And heaven knows we don't need to give motorists any more excuses to try to run us off the roads.
Specificity is an important element of training for any sport. Every sport requires (in some measure) the basic elements of strength, speed, and endurance. So every serious, successful athlete trains all three, at least a little bit. I remember having to run a mile and a half in football conditioning (hated it). But we spent a lot more time lifting weights for football, because strength is way more important than endurance when you're only running far enough to hit the person directly across from you.
You could probably have figured this out on your own, but triathlon is primarily a sport of endurance. Hence long bikes, long runs, long swims. Coincidentally, of strength, speed, and endurance, the most effective training is to put endurance first, then strength, then speed. But that doesn't mean that triathletes never need to work on strength, or on speed.
If you've been doing this sport long enough to want to get better, you've been in it long enough to know you can go the distance. You've got the endurance to run a 10k or bike 50 miles or whatever the case may be. What you don't have is speed at those distances.
Here's where the specificity comes in. Let's say you want to be able to run a 10k in under 60 minutes. That's a pretty good goal, right? So you need to run 6.2 miles at a sub-10:00-minute pace. But you do all of your training runs at a pace of around 10:15/mile. Now there's definitely something to be said for race-day adrenaline, or whatever it is that allows us to outperform our best training at a big event. But if you can't do a 3-mile tempo run at 9:40 pace, what makes you think you're going to be able to go twice that far after swimming and biking for an hour?
It's been my experience that you get so comfortable with your long, steady pace when you're training endurance that it can be hard to shift out of that gear and into a speedier one. I started paying a little bit closer attention to my heart rate on training runs, and realized I wasn't getting my heart rate up quite as high as I was supposed to. I had built a really good base, had good endurance, and that had prompted better efficiency and less effort at my base-building pace. One day, during a mid-distance run (probably 6 miles), I decided to push a little bit to see what it would take to get my heart rate in the target zone. Ended up doing my six-mile run on about a 9:20 pace. I'd been doing all my runs right around 10:00. Had no idea I could hold 9:20 for 6 miles. After that, I was more willing and able to push on my runs, especially the long ones.
Practically speaking, there are a few things you can do. Train with a heart rate monitor. Know your heart rate zones. And know which one you need to be in for each workout.
Pace is a little bit trickier to measure, at least on the run (if you have a decent cycle computer on your bike, you're set); generally, you don't know what your pace was until you can get a split, whether that's at a mile marker or half mile marker or what have you. If you want to drop some money to improve your training, you could always get a fancy-schmancy GPS device that'll tell you your pace while you're running. But that's not strictly necessary. What you can do is have a sense of where in your run you are. If there's a Dunkin' Donuts half a mile into your run, you should know that. And not so you can stop for a little carbohydrate pick-me-up, but so you can check your watch and say to yourself, "Okay, 4:50 for that first half mile; that's probably about right." Or pick it up/slow it down appropriately.
There's more to specificity of training than what I've covered here, of course. But we want to look at the things that'll make you faster in a big-picture sense, and making sure you hit the appropriate training intensity and pace in your workouts will do that for you.
A quick note: this article is written mostly from the point of view of improving the run. When trying to hit the right numbers on your bike, you'll need to pay attention primarily to your heart rate or power meter (if you have one), because speed is so variable depending on wind and terrain. With swimming, you'll want to watch your pace more carefully, because heart rate can be unreliable underwater. Something to do with vascular pressure.