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"La hora" is a form of "hora", a noun which is often translated as "hour". "Cuarto" is an adjective which is often translated as "fourth". Learn more about the difference between "la hora" and "cuarto" below.
la hora()
A feminine noun is almost always used with feminine articles and adjectives (e.g., la mujer bonita, la luna llena).
a. time
Es hora de que se reúnan y tomen una decisión.It is time for them to meet and make a decision.
5. (meeting)
a. appointment
Mañana tengo hora con el podólogo.I have an appointment with the podiatrist tomorrow.
cuarto, el cuarto()
An adjective is a word that describes a noun (e.g., the big dog).
a. fourth
Entra al edificio y toma el ascensor al cuarto piso.Enter the building and take the elevator to the fourth floor.
A masculine noun is used with masculine articles and adjectives (e.g., el hombre guapo, el sol amarillo).