This is a standard formation that is similar to the standard military parade formation your units automatically enter after creation. Switching to delta formation positions your units in a flat triangle formation. The flat nature makes it easy to select specific craft when looking from overhead, but it isn't very useful in concentrating firepower on an enemy. Use the delta formation when moving your forces to the battle and separate them into new formations and functions as you arrive on the scene.
Broad, like delta, is similar to the standard military-parade formation. Unlike delta, broad simply forms the ships in a straight and flat line. This again makes it easy to select specific ships. It's best used for capital ships, so you can easily micromanage them during a battle. Don't bother with broad for strike craft.
One of the best formations for strike craft, X positions your forces in a 3D X formation. It places the craft in a relatively tight formation, which does have its disadvantages. The strike craft will have a tough time evading enemy fire. The X has an advantage over claw in large numbers because, in the X formation, all your strike craft stick together - some strike craft won't arrive before others in your squad.
Claw formation is similar to X in its capabilities. Once again, it's excellent for strike craft and offers a tad more maneuvering room than the X formation. Because of its 3D shape, claw is best used against capital ships. The formation lets the strike craft envelop the capital ship, presenting multiple targets from multiple sides. Don't use claw with a large number of strike craft. Claw is best when used with 20 to 30 strike craft. If you use a larger number, the claw formation becomes too profound. The lead ships will fly much too far from the rear vessels. This brings you into the attack at a numbers disadvantage, which typically leads to a defeat.
As its name suggests, the wall formation places your group in a square or rectangular vertical formation. The formation is somewhat similar to X in its concentration of firepower and its weakness against evading enemy fire. Many players prefer the wall formation when using strike craft to attack smaller capital ships (such as the multibeam frigate). If the enemy has little defense against strike craft, the wall's concentration of fire can prove deadly.
Watching the sphere formation in effect is a sight to behold. Your craft will position themselves in a sphere formation around the intended target (or the craft you've selected to guard). Your craft will remain stationary as they fire upon the enemy ship from that position. If they remain stationary, they become easy targets for capital ships, so use the sphere formation against non-hostile targets like workers - unless you have enough strike craft to take down the capital ship quickly.