AgentWorkSkill(Agent Work Skill) object/entity in Salesforce Omni-Channel represents skills used to route a work item to an agent. This object/entity is mainly used for reporting purpose. It contains the dropped skills also during routing. It is tied to the Agent Work object/entity.

AgentWorkSkill(Agent Work Skill) records are created after the AgentWork(Agent Work) record creation.

Sample SOQL:

SELECT AgentWorkId, WasDropped, 
Skill.DeveloperName, SkillLevel, 
SkillPriority
FROM AgentWorkSkill
WHERE AgentWorkId IN (
	SELECT Id
	FROM AgentWork
	WHERE WorkItemId = '5004W00002XZAcSQAX'
)

In the above SOQL, we are fetching all the Skills that were used to route the Case record.