I wanted to know what is the meaning of "checking off the points upon the palm of his left hand"?

I think that Holmes (note the capital letter) was imagining that the list of points he wanted to make was written on his hand, and pointing to each one as he spoke of it.

1. Open your left hand with your palm upwards and facing your face.

2 Make a fist of your right hand, and

3 then extend your right index finger.

4 Place the tip of your right index finger on your left palm at the base of the left thumb.

5 Now move the tip of the right index finger down towards the centre of your wrist and then, quickly

6 Move the index finger upwards towards the tip of your left ring finger.

You have drawn a "tick" on the palm of your hand.

Holmes was making this movement each time he mentioned a significant point in his story. This is called checking off (a tick is also known as a check mark.) He does this so as to remind himself that he has mentioned each significant point.

An extract from the previous paragraph. Holmes is speaking to Watson:

"At least I have got a grip of the essential facts of
the case.  I shall enumerate them to you, for nothing
clears up a case so much as stating it to another
person [...]."

Holmes is enumerating a number of points. Perhaps he accompanies the successive points by putting successive fingers (or one finger, then two fingers etc.) of his right hand down upon the palm of his left hand.