vs
QUICK ANSWER
"Invitarle" is a form of "invitar", a transitive verb which is often translated as "to invite". "La" is a definite article which is often translated as "the". Learn more about the difference between "invitarle" and "la" below.
invitar(
een
-
bee
-
tahr
)A transitive verb is a verb that requires a direct object (e.g., I bought a book.).
a. to invite 
Voy a invitar a toda mi familia a mi fiesta de cumpleaños.I'm inviting my whole family to my birthday party.
2. (to pay)
b. to take out 
No es mi novia. Solo la invité a cenar.She's not my girlfriend. I just took her out to dinner.
3. (to attract)
a. to entice 
El ambiente de ese bar invita a bailar.The atmosphere of that bar entices you to dance.
An intransitive verb is one that does not require a direct object (e.g., The man sneezed.).
4. (to pay)
c.  no direct translation
This refers to an idiomatic word or phrase for which there is no word-for-word translation.
Tomen algo. Invitamos nosotros.Have a drink. It's on us.
Guarda el dinero. Invito yo.Put your money away. It's my treat.
la(
lah
)A definite article is a word that identifies a noun as specific or known to the speaker (e.g., the girl).
a. the 
La pelota está en el tejado.The ball is on the roof.
La leche está en el refrigerador.The milk is in the refrigerator.
A pronoun is a word that stands in for a noun (e.g., she).
A masculine noun is used with masculine articles and adjectives (e.g., el hombre guapo, el sol amarillo).