I have never seen an explanation for the Spanish word "He".
Here is an example,
He prometido guardar Tus palabras.
Can someone please explain this to me?
It's exactly the same as "Have" in english. "He" is a verbal tense of the verb "haber".
(In your example, in english, "I have promised...")
Where is the doubt?
Maybe you are missing the subject, the person; in spanish you can skip it because it's implied in the verbal tense itself (Yo he, Tu has, Él ha, etc.), but it would be also correct to say "Yo he prometido guardar"...
Hope that helps.
You're thinking that "He" acts as the subject, aren't you? Well, it's not. It's the verb (In fact "He prometido" is the verb)
In Spanish you can apply an pronoun ellipsis when it acts as the subject. For example, you can say:
Yo escribo una carta
Escribo una carta.
In your example (He prometido) you're using a compound tense of the verb "Prometer" (which is formed with the auxiliary tense of verb "Haber" + the past participle of verb "Prometer").
Here you can also apply the pronoun ellipsis rule if you want (which is very common to do it):
Yo he escrito una carta.
He escrito una carta.