Can you provide an example?

Isn't "parce qu'on voit les gens souffrir" the example?

Isn't "parce qu'on voit les gens souffrir" the example?

Oh, silly me, I must have missed themsecomd line. Sorry. 

The point of this lesson is to demonstrate the use of the infinitive for some continuous form constructions in English. In the example you cite, "voit" is the verb and "souffrir" is the infinitive (sufferING). 

Parce qu'on voit les gens souffrir. -- Because one sees the people suffering. 

-- Chris (not a native speaker). 

That is what I thought. So instead of "La fille qui joue du piano est mon amie" Could I use "La fille jouer du piano est mon amie"

No, that would be incorrect. It isn't that the French infinitive simply corresponds to the English present continuous form. Rather, the French present tense can often times also be translated as present continuous in English.

The girl who plays the piano is my friend. -- La fille qui joue du piano est mon amie.
The girl playing the piano is my friend. -- La fille en jouant du piano est mon amie. (you'd need a gerundive in French)

But to demonstrate it in a simpler sentence:

La fille joue du piano -- The girl plays piano. And also: The girl is playing the piano.

The problem is that in English the gerundive of a verb is identical with the "-ing" form.

The girl playing the piano. -- Here "playing" is the gerundive.
The girl is playing the piano. -- Here "playing" is present continuous tense.

I don't know if that makes it any clearer, though....

-- Chris (not a native speaker).

Yes, it does make it a little clearer. Thanks! Can I ask another question? Is "jouant" ever used by itself without "en"?

Without the "en", you have yourself a present participle. It is less frequently used than its counterpart in English but it is being used.

Elle est partie, oubliant ses clefs. -- She left, forgetting her keys.
Elle est partie en oubliant ses clefs. -- (sounds silly) She left by/while forgetting her keys.

Most often, the present participle is used as an adjective: charmant, intéressant, courant, stressant, etc.

In this context, it is useful to note the change in meaning between the following pairs of adjectives:

stressant -- stressé: stressing (stressful) -- stressing
intéressant -- intéressé: interesting -- interested

Greetings, -- Chris (not a native speaker).

Thanks your your help, the two sentences about keys illustrates the differences. Thanks again! Cheers!

" La fille en jouant du piano est mon amie" sounds odd to me. Are you sure it's possible to say this?

It sounds pretty stilted to my ears but it would be grammatically correct. You'd never hear it said, though, I believe. 

-- Chris.