When Obi-Wan Kenobi first appears in Star Wars IV - A new Hope he scares a bunch of sand people away and then he proceeds to check Luke Skywalker, first by checking his pulse and then he sticks his hand on Luke's face as if he's checking something else. What was he doing?
Picture for added reference.
Obi-wan actually puts his hands on a lot of people's faces.
In Episode I, at the Invasion of Naboo, after Qui-Gon and Darth Maul's battle/death, Obi-wan is there for his master.
In Episode II, at the Battle of Geonosis, when the Jedi are surrounded by the droid army, he is seen with his hands on the face of a fallen Jedi.
In Episode III, on Mustafar, after Padme passes out from Anakin force choking her, Obi-wan puts his hand on her face.
I can only assume that he is checking on the person's condition by putting his hand on their face/forehead area. Possibly he is checking for a sign of life with this technique, similar to how we check for a pulse.
In the Star Wars Roleplaying Game - Revised core Rulebook the moment you refer to is used as an illustration of the Heal Another light side force-skill (p091).
The book has this to say about the skill:
Stabilize a dying character
Restore (various amount of) vitality points
You must touch the target
Maybe this is not a reference that can be read as canonical, but it gives some insight on what Obi-Wan may have intend to do.
This scene is mentioned in the Young Reader Classic adaptation of A New Hope, not to be confused with the film's junior novelisation.
The strong implication is that Luke had suffered a head injury of some description (perhaps a concussion?) and Obi-Wan used some sort of Force power to heal him, or at least to bring him back to consciousness:
Strange! An old man had frightened them off. He bent down beside the fallen boy. Then he touched him. It was a gentle touch. Yet it seemed to have the power to open Luke’s eyes. Luke found himself gazing up at the kind face of the hermit, Ben Kenobi.
For completeness, I should mention that the incident is mentioned in the script...
Artoo waddles over to were Luke lies crumpled in a heap and begins to whistle and beep his concern. Ben puts his hand on Luke's forehead and he begins to come around.
...but that no explanation is given for why he does it, only the effect.
Maybe it's some of Force induced healing. For Luke he puts his fingers on the temples rather than sensing the pulse on the neck, like in other picture. Luke regain consciousness almost immediately. In Star Wars RPG there is a skill (Heal Another) that could be just like that.
fI'd first like to note that the earliest games to be based around Star Wars - West End's d6 SW RPG and Decipher's Star Wars RPG, despite both having access to lots of background material, including Lucas's notes, never mention Force Healing as a thing. They're also relatively uncorrupted by later additions to the series (both predate the prequels, and West End's game even predates the expanded universe). They're both pretty scrupulous in maintaining accuracy to the movie universe, too. That neither of these sources ever references some sort of generic Force healing as a thing is pretty conclusive that no such power is referenced in either the movies themselves or the script or background notes. (And in fact, West End's SW sourcebooks are some of the best 80s source material for official background material because of the extensive access they got to otherwise unpublished documents at the time).
It's also not clear that Luke even needs healing in that scene in A New Hope. He's been knocked unconscious. There's no bleeding or other obvious trauma. (Which doesn't make a more serious injury impossible, just that we have no evidence one way or another).
A far better interpretation of the scene is that Obi-wan is checking to see if Luke's okay - not by searching for a pulse, but by using a Force power we know exists (sense) to check Luke's mental state. He determines Luke doesn't need medical care, and then shakes him a little to help him come to (after speaking to R2).
Possibly also noteworthy - the musical cues are not suggestive of healing Force powers at that point in the scene. The music has an edge of danger, emotionally pushing us towards wondering if Luke will be okay, and suggesting Ben is wondering the same. It's only as Ben tells R2 that he'll be fine that the music switches over to the Force/Obi-wan theme (it was obi-wan's theme in ANH, it only gets reified into the Force theme in later movies). If Obi-wan was doing something proactive with the Force at that point, you'd expect the musical cues to have shifted into Obi-wan's theme already.
