Sending packets is the way that the server communicates with the clients.
When you perform an action ingame like leveling up a skill, attacking a monster or even just targeting a monster, your client will send a packet to the server. When the server receives your packet, it validates the information (for example, it checks if you have enough skill points to level the skill) and then sends a response, which is also a packet. When the client receives the response, it will show you that the action was completed.
Example:
Code:
C->S: Level Up Skill to level 3
if (player has enough skillpoints to level up)
S->C: Level Up Accepted
else
S->C: Level Up Denied