The verb gustar behaves like English „please” or „be pleasing”.
Me gusta la casa – I like the house, the house pleases me
Me gustan estos zapatos – I like these shoes, these shoes please me.
That's why it mostly appears in the third person, unlike English „like”.

The form of „gustar” will depend on „what he likes”, not on the subject in English, exactly as if we used the verb „please” :
Le gusta esta cosa – He/she likes this thing, this thing pleases him / her.
Le gustan estes cuartos – He likes these rooms, these rooms please him

This form (me, te, le) is an indirect object pronoun. If the indirect object is a noun, it should be preceded by the preposition "a" and the form le (in plural les) should be added :
A Juan le gusta esta casa – Juan likes this house, this house pleases (to) Juan.
A usted le gusta leer - It pleases (to) you to read, You like to read.
A los niños les gustan estos zapatos - The children like these shoes, These shoes please (to) the children.
A los niños les gusta esta casa - The children like this house, This house pleases (to) the children.

If the indirect object is a pronoun, it is possible to repeat it for emphasis - then we will have forms : a mí me gusta, a ti te gusta etc. :
A mí me gusta la casa. A mí me gustan estos zapatos. A ti te gusta esta cosa.

There are more verbs like this in Spanish , for example :
encantar : Me encanta su voz - I love her voice / Her voice enchants me.
In English, verbs like seem (it seems to me) or appear behave similarly.