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"Gestión" is a noun which is often translated as "management", and "emprendimiento" is a noun which is often translated as "undertaking". Learn more about the difference between "gestión" and "emprendimiento" below.
la gestión(
hehs
-
tyohn
)A feminine noun is almost always used with feminine articles and adjectives (e.g., la mujer bonita, la luna llena).
1. (business)
2. (politics)
a. administration 
En general, su gestión dejó al país en buen estado.Overall, his administration left the country in good hands.
3. (procedure)
a.  no direct translation
This refers to an idiomatic word or phrase for which there is no word-for-word translation.
Tengo que hacer unas gestiones en el centro de la ciudad.I have to do some business downtown.
Estamos a punto de terminar las gestiones para comprar la casa.We've almost finished the process of buying the house.
el emprendimiento(
ehm
-
prehn
-
dee
-
myehn
-
toh
)A masculine noun is used with masculine articles and adjectives (e.g., el hombre guapo, el sol amarillo).
a. undertaking 
El emprendimiento del proyecto solo fue posible tras recibir fondos del gobierno.The undertaking of the project was only possible after it received government funding.
a. undertaking 
El éxito de este nuevo emprendimiento depende del esfuerzo conjunto de todos los que trabajamos en él.The success of this new undertaking depends on the joint effort of everyone working on it.
a. entrepreneurship 
Ese joven se destaca por su emprendimiento y su compromiso con la comunidad.That boy is unique for his entrepreneurship and his commitment to the community.
b. initiative 
Juan es un hombre de emprendimiento y pronto se recuperará de esta quiebra.Juan is a man of initiative who will soon recoup his losses from the bankruptcy.