What is the reason that intercourse is required for a valid marriage? Within the Catholic Church, it is required to have intercourse with each other after marriage. But what is the reason behind this?
Intercourse is not necessary for the validity of a marriage.
The essence of marriage is the matrimonial consent (exchange of vows), not sexual intercourse.
St. Thomas Aquinas explains in Summa Theologica suppl. q. 42 a. 4 that carnal intercourse is not an integral part of marriage; in Summa Theologica III q. 29 a. 2 he explains how Sts. Joseph's and Mary's marriage was a true marriage, despite being a virginal marriage.
However, the ability to have intercourse is necessary for the validity of marriage. Permanently impotent people, for example, cannot validly contract marriage; impotency is an example of a diriment impediment, which is

A condition, circumstance, or situation that makes an action null and void in its intended effects. Thus an existing marital bond nullifies any attempt to enter a second marriage.

Canons 1083 ff. list all the diriment impediments that render marriage invalid.
Consummated vs. Unconsummated Marriages
These can both be valid marriages.
Consummated
A consummated marriage is

A marriage in which after the matrimonial contract is made husband and wife have marital intercourse. Contraceptive intercourse does not consummate Christian marriage. (Etym. Latin consummare, to bring into one sum, to perfect.)

In canon law, such a marriage is called ratum et consummatum (&quot;ratified and consummated&quot;). Only death dissolves the bond:

Can. 1141 A marriage that is ratum et consummatum can be dissolved by no human power and by no cause, except death.

Unconsummated
An unconsummated marriage is called ratum sed non consummatum (&quot;ratified but not consummated&quot;). Unconsummated marriages can be dissolved by the Pope if either or both parties decide to enter religious life. This is the so-called Petrine Privilege, because it requires the Pope's permission:

Can. 1142 For a just cause, the Roman Pontiff can dissolve a non-consummated marriage between baptized persons or between a baptized party and a non-baptized party at the request of both parties or of one of them, even if the other party is unwilling.