The french verb dégager and its past participle dégagé are common words with several distinct meanings. Their use ranges from the physical to the figurative, and from formal to very informal.

The verb: dégager

At its root, dégager means to free something or someone from an obstacle or obligation. It is the opposite of engager (to engage, to commit).

1. To clear or free a space
This is the most literal meaning. It involves removing things that block a path or area.

• Il faut dégager la table après le dîner.
  One must clear the table after dinner.
• Les pompiers ont dégagé la route.
  The firefighters cleared the road.
• Dégagez le passage, s’il vous plaît.
  Clear the way, please.

2. To give off or emit
It is used to describe smells, heat, or light coming from something.

• Les fleurs dégagent un parfum doux.
  The flowers give off a soft scent.
• Le moteur dégage de la chaleur.
  The engine gives off heat.

3. To free from an obligation
In a legal or formal sense, it means to release someone from a promise or duty.

• Ce document vous dégage de toute responsabilité.
  This document frees you from all responsibility.
• Il cherche à se dégager de son contrat.
  He is seeking to get out of his contract.

4. To free a part of the body
Often used in a physical or medical context.

• Le kiné m’a aidé à dégager mon cou.
  The physio helped me free up my neck.

5. To abstract or separate an idea
Used in a figurative sense, it means to identify or isolate a concept.

• On peut dégager une idée principale de ce texte.
  One can draw out a main idea from this text.

6. Slang: To get lost or go away (rude)
This is a very common and forceful use of the verb. It is an order to leave immediately.

• Dégage !
  Get lost! / Piss off!
• Il m’a dit de dégager de chez lui.
  He told me to get the hell out of his place.

The past participle: dégagé

When used as an adjective, dégagé describes something that is free, clear, or unobstructed.

1. A clear view or space

• D’ici, nous avons une vue dégagée sur la vallée.
  From here, we have a clear view of the valley.
• Cherchez un endroit dégagé pour garer la voiture.
  Look for a clear spot to park the car.

2. Clothing that is open or revealing (neckline)
It describes clothing that leaves a part of the body, usually the neck and shoulders, uncovered.

• Elle porte une robe au col dégagé.
  She is wearing a dress with an open neckline.
• Une tenue dégagée pour l’été.
  An outfit that is light and free for summer.

3. A relaxed or free manner
It can describe a person’s attitude as being casual and without worry.

• Il a un style dégagé et naturel.
  He has a relaxed and natural style.

Synonyms and alternatives

• For to clear a space: débarrasser (to clear, to tidy away), libérer (to free up).
• For to give off (a smell) : exhaler (to exhale, to give off), répandre (to spread).
• For to free from an obligation: libérer (to free), dispenser (to exempt), exonérer (to exempt, often financially).
• For slang (get lost) : casser (as in casse-toi, a slightly less harsh way to say get lost), ficher le camp (to clear off), partir (to leave).
• For clear (view) : clair (clear), libre (free), ouvert (open).

Summary

• Dégager is a verb with meanings that range from clearing a physical space to emitting a smell, or releasing someone from a duty.
• It has a very strong slang meaning as a rude command to leave.
• The adjective dégagé describes something that is free, unobstructed, or an attitude that is relaxed and casual.