"Battles are won by slaughter and maneuver. The greater the general,
the more he contributes in maneuver, the less he demands in slaughter."
Being the more mobile army essentially grants you superiority during the movement phase. This can be achieved through the use of mobile troops (those equipped with bikes or jumppacks, or mounted), or, if your troops are not naturally mobile, by buying them transport vehicles. Even a slim advantage, such as the d6 inches granted by a fleet move, can be exploited to grant mobility superiority.
Some examples of superior mobility armies would include the mechanized Tau (lots of skimmer transports and jump infantry), the Kult-of-Speed (lots of fast vehicles, bikers), the Dark Eldar (lots of fast transports) or the Ravenwing marine (all bikes and landspeeders) chapter.
Some armies with notable lack of mobility include Necrons (almost no potential for transports) and the Daemonhunters (very few transports). Both of these armies can use some deep-striking tricks to get a semblance of mobility, but this is far from reliable.
What is the impact of having a superior mobile army? Well, if you have a more mobile army than your opponent, it largely means that you get to fight the battle on your terms, not theirs. If you can run away from them, they cannot engage you where you don't want to be engaged. If you can make quick moves to engage them, you get to choose what parts of their army to fight. The best way to exploit superior mobility is to use it to isolate small parts of your enemies force and address them independently. Having a more-mobile army is also likely to give you more turns before you have to run your troops over to objectives that you may need to capture. Another advantage of having movement superiority is that it is the phase where the dice are least-likely to impact the game, so if you're used to rolling poorly, concentrating on movement may be for you.
The cost of mobility is generally high. Transports can cost 50 points or more. Jump infantry or bikes can cost twice what a normal infantryman costs. You pay a premium in points for the ability to be mobile. If you're putting all those points into your mobility, you're going to have less points to spend on actual combat ability. So, you cannot afford to engage in a straight-up fight because you will be outnumbered. So this means that you have to try and pick off the parts of your opponent's army that are isolated.
My little brother is in the US Army. He says that current US Military doctrine is not to engage enemy forces unless they have a three-to-one numerical advantage. You're rarely going to be able to pull that off, even with a highly mobile force, but the concept is sound. If you send one mobile squad against one enemy squad, odds are good that even if you kill the enemy, you'll take enough casualties during the engagement that your unit won't contribute much to the rest of the battle, or won't count as scoring at the end. If you can take two squads against one enemy squad, they're going to take twice the initial casualties, and have only half the attacks to throw back at you.
By extention, if you are fighting an army that is more mobile than your own, you need to attack their weaknesses. They will have less guys than you, if you keep your guys together. If your opponent is more mobile than you, don't send units off alone (unless you have a crafty plan), because that's what they want you to do. They are just waiting for easy pickings left apart from the rest of the force. You should also attack the enemies mobility. If they paid a lot of points for transports, and you destroy the transports, they're going to be stuck walking around the battlefield, with less guys than you have.
Finally, if you have one or two mobile units in an otherwise less-mobile army, you should think twice about charging them forwards alone and without support. It isn't always a bad idea - if you can get one mobile assault unit into combat, do so. But, doing so without thinking about what your opponent's response will be is a good way to leave that mobile unit stuck out in the open, surrounded, and killed.
"If the enemy is to be coerced, you must put him in a situation that
is even more unpleasant than the sacrifice you call on him to make. The
hardships of the situation must not be merely transient - at least not
in appearance. Otherwise, the enemy would not give in, but would wait
for things to improve."
So, if you're playing a more-mobile army, and your opponent knows it, how do you get their units separated? One trick can be so set up a false-front during deployment. If there is more than one objective in the game, set up half of your army in a position to capture one of them, and half in a position to capture the other. If your opponent takes the bait, they will do something similar, looking to contest both the objectives. On your first turn, you take your mobile elements from one side and swing them across to back up the other side. Your opponent's less-mobile forces are left separated, and you can then take your whole army and wipe out each half of his army separately. This is a classic refused flank maneuver (you refuse to engage your opponent on one flank, instead concentrating on the other).
Another possibility is to use a bait unit, dangling it just out of reach of your opponent's army. You need to estimate "just out of reach" carefully, or you lose the bait. As your opponent approaches the bait, you pull it back, and move other support units to assist it. The units that your opponent sent to deal with the bait can then be addressed separately from the rest of their force.
Finally, you can offer your opponent a damned-if-you-do/damned-if-you-don't situation. One example of this is taking a looted ordnance tank in a Speed Freak army. If your opponent bunches up to defend against being isolated, the ordnance weapon becomes much more useful, as it can kill many units, and if it scatters, it is likely to still hit something else. If they spread out to avoid the ordnance shots, they run the risk of having their flanking units destroyed by the more mobile orks.
How do you know who is more mobile? Several armies have the capability to be either highly mobile or totally immobile, depending on what unit choices they make. With a few exceptions, you're not really going to be able to guess based simply on what army they're playing. While sometimes knowing your opponent's army will give you a good guess, an eldar army based around guardians, reapers, scorpions and D-cannons is almost immobile, while an eldar army based on falcons, waveserpents and vipers is the epitome of mobility. You need to pay attention to the elements of your opponent's army, and compare them to the overall mobility in your army. I've listed a bunch of unit-types below, in order of mobility from best to worst. If your units are generally higher than your opponent's, then you're the more-mobile army.Mobility, from best to worst:
Finally, there are some tricks, like deep strike and infiltrate that allow an army to gain a semblance of mobility for the deployment of their units. While this isn't true mobility, as the units are left with normal movement after they are placed on the table, it can be used to offset some of the disadvantages of low-mobility. An army facing an all-infiltrating or all-deepstriking opponent should consider itself to be the less-mobile army until the enemy units are on the table, or risk losing local superiority as the enemy focuses on only half of your force.