When discussing the Trinity, we can see that the three persons are of the same essence and One God. In the Nicean creed we profess that the Holy Spirit proceeds from the Father and the Son. This mission of divine persons can be seen directly in their processions. Through this mission of procession, we can see their unity and equality. Through this unity and equality is their ultimate end of the redemption of mankind (Garrigou-Lagrange Ch. XVII).
Mission involves the sending of someone from another and is made up of being send from a specific destination, to a specific destination, and a link between the two. To process in mission from one is an implication of equality. In the military troops are sent forth to another region. They do not represent themselves, but the nation to whom they belong. If they do something wrong, it is as if the whole nation has done something wrong. Though this may not be the best example, especially regarding the Trinity, it makes the point that the procession of divine persons is equal to the sender. They are worth no less than the one doing the sending.
In the persons of the Trinity the Father is not able to be sent, but the Son and the Holy Spirit can be. The divine persons being sent do not cease to be where they are or where they are going. They have always existed and will continue to be. They are God and thus are omnipresent and omniscient. This procession in mission is done for the purpose of our very sanctification.
Garrigou-Lagrange, Reginald. The Trinity and God the Creator. https://www.ewtn.com/library/THEOLOGY/TRINITY.HTM#00, accessed December 12, 2018