*sigh* Alright, welcome Class, to PSI 101.
What is PSI? PSI is basically any form of psychic power, which can be used for various purposes, at the cost of PP (Psychic Points).
What is PP? Basically the MP (Magic Points) of the Mother/EarthBound universe that is consumed whenever PSI is used. It's not to be confused with Power Points used by Pokemon to use their attacks.
What can PSI be used for? Just about anything. It can be used offensively in the form of an element or generic energy. It can be used to heal wounds or cure/cause abnormal status. It could even be used to manipulate the strength/defense levels of yourself or another. Here is a list of basic PSI abilities common to the Mother games:
~Offense~
Fire - A fire attack, usually targets enemies in an entire row. Not entirely useful unless the enemy is weak against fire.
Thunder - Basically a bolt of lighting. It can target enemies in a column. A bit more useful than Fire, but still about the same.
Freeze - The most useful of the 3 elements. It targets a single enemy, and can deal more damage than either Fire or Thunder. Furthermore, it also has a chance of freezing the target solid for a certain amount of time.
Flash - A flash of light that can deal minor damage and temporarily blind the enemy.
Rockin - Pretty much generic damage to all enemies. This is Ness' primary PSI attack in EarthBound.
Love - Same thing as Rockin, only it also allows the user to pull one of the seven needles that keeps the Dark Dragon asleep. This attack primarily belongs to Lucas and Claus.
Starstorm - This is incorrectly portrayed as Ness and Lucas' ultimate attack in Brawl. However, it's no more powerful than Rockin and Love, and can only be used by Ness' friend Poo.
~Recovery~
Lifeup - Heal wounds (HP)
Healing - Cure abnormal status (Sleep, Poison, etc)
~Assist~
Offense Up - Raises target's physical attack damage.
Offense Down - Lowers physical attack of the target.
Defense Up - Raises target's physical defense damage.
Defense Down - Lowers physical defense of the target.
Hypnosis - Puts target to sleep (doesn't always work)
Shield - Raise defense against PSI/magic. More powerful shields can deflect attacks back at the sender.
Teleport - Allows user to teleport from one location to another (usually towns they have already visited)
Now, there are 4 power levels to each PSI ability. A different power level means a more powerful effect. These four levels are named after Greek alphabet: Alpha (L1), Beta (L2), Epsilon (L3), and Omega (L4). Some PSIs, like Healing, produce a different effect based on level. For example.
Lifeup Alpha - Heals some wounds on a single person (usually around 40-50 HP worth)
Lifeup Beta - Heals more serious wounds on a single person (Usually about 100-150 HP worth)
Lifeup Epsilon - Heals wounds on multiple targets (Around 80 HP to entire party)
Lifeup Omega - Heals multiple targets (Usually about 150-200 HP to entire party)
Healing Alpha - Cure poison/cold
Healing Beta - Cure sleep/crying
Healing Epsilon - Revive fallen comrade from KO status
Healing Omega - Cure all abnormal status (except KO)
In EarthBound, Ness' PSI were as follows by the end:
~Offense~
Rockin (All LVs)
Flash (All LVs)
~Recovery~
Lifeup (All LVs)
Healing (All LVs)
~Assist~
Offense Up (All LVs)
Offense Down (All LVs)
Shield (All LVs)
Teleport (All LVs)
Lucas' PSI by the end of Mother 3 was pretty much the same, only PK Love replaced PSI Rockin.
I hope this has been of interest, and taught you a little more about how Ness and Lucas function in Brawl. Class dismissed.