Artillery refers to units that lob highly damaging and explosive shells over a large arc to a target, going over hills and other obstacles. The mobile versions do not have nearly as much range as the stationary versions, however have much higher DPS per mass invested.
Typically, the purpose of mobile artillery is to disrupt large forces of enemy units. Their relatively large damage area, and high initial damage make them very effective against clustered enemies. They can also be used to good effect in base assaults. Mobile artillery is capable of outranging any point defenses of equivalent tech level, making them invaluable against defensive positions which have not yet been fully established. However, once a defending player has constructed stationary artillery, they are typically quite safe from enemy mobile artillery, which, even at tech 3, cannot match the range of a tech 2 artillery emplacement.
Mobile artillery tends to have very low health, and, as a rule, no defense against air units. This means that bombers, and especially gunships can take them down with ease. Therefore, it is advisable to protect them with mobile anti-air units. Mobile shield generators are also strongly recommended, as the artillery's low health can make them easy targets, despite anti-air support. For the especially concerned player, some direct fire units can be useful in case of a ground attack, though large quantities of mobile artillery tend to negate the risk.
When encountering enemy mobile artillery, an all-out rush is rarely a good idea, as their large damage and spread can make quick work of your land forces. Against a skilled player, your units will run through the enemy barrage, only to arrive heavily damaged, and fall quickly to their own direct-fire units.
Gunships are a very effective counter to enemy mobile artillery, and can quickly tear through their lines. Skilled players will likely also have some AA in the vicinity, making bombers more favourable. Being able to do all their damage at once allows them to destroy the threatening artillery, and then fly away before enemy AA can finish them off.
Ironically, one of the best counters to enemy mobile artillery is having some of your own. While the enemies' attention is elsewhere, a small contingent of your artillery can make short work of theirs. Artillery emplacements are a reliable defense against mobile artillery, being able to outrange them, regardless of tech level.
If all else fails, adhere to Supreme Commander's generally accepted Rock-Paper-Scissors format (land beats air which beats navy, which beats land). No mobile position can hope to withstand bombardment from equivalent naval units. Their high costs and build times can be prohibitive as a responsive countermeasure however, so some should always be kept in reserve, should the need for them arise.