Aloe plants do not shed seeds like other plants. They duplicate by sending little "shooters" off of their roots.
You can separate the baby Aloes from the larger Aloe by gently untangling the roots and separating the "baby" from the "mom."
Repot your bigger Aloe in a larger pot, and put your babies in smaller pots! Or give them to friends and family as gifts.
Fun fact: we got our first Aloe plant from someone who was giving away little baby Aloe plants. We usually give them as teacher gifts at the end of the year with a cute banner that says "Thanks for Helping me Grow!"