Before looking into dictionary definitions and synonyms, what does respect mean to me:

1. listening without interrupting
2. taking the others feelings into consideration
3. keeping an open mind
4. agreeing to disagree
5. trying to understand the others viewpoint
6. direct communication
7. building a person up instead of tearing them down
8. faith in the other persons decisions and abilities
9. celebrating differences
10. making the other person a priority

Relevant meaning of Respect, according to Webster’s Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.

1. To take notice of; to regard with special attention; to regard as worthy of special consideration; hence, to care for; to heed.

2. To consider worthy of esteem; to regard with honor.

4. To regard; to consider; to deem.

As respects, as regards; with regard to; as to. –Macaulay.

To respect the person or persons, to favor a person, or persons on corrupt grounds; to show partiality.

Syn: To regard; esteem; honor; revere; venerate.

according to Random House Unabridged Dictionary, © Random House, Inc. 2006.

–noun
3.    esteem for or a sense of the worth or excellence of a person, a personal quality or ability, or something considered as a manifestation of a personal quality or ability: I have great respect for her judgment.
4.    deference to a right, privilege, privileged position, or someone or something considered to have certain rights or privileges; proper acceptance or courtesy; acknowledgment: respect for a suspect’s right to counsel; to show respect for the flag; respect for the elderly.
5.    the condition of being esteemed or honored: to be held in respect.
7.    favor or partiality.
–verb (used with object)
9.    to hold in esteem or honor: I cannot respect a cheat.
10.    to show regard or consideration for: to respect someone’s rights.
11.    to refrain from intruding upon or interfering with: to respect a person’s privacy.

Synonyms

1. regard, feature, matter.
2. regard, connection.
3. estimation, reverence, homage, honor. Respect, esteem, veneration imply recognition of personal qualities by approbation, deference, and more or less affection. Respect is commonly the result of admiration and approbation, together with deference: to feel respect for a great scholar. Esteem is deference combined with admiration and often with affection: to hold a friend in great esteem. Veneration is an almost religious attitude of deep respect, reverence, and love, such as we feel for persons or things of outstanding superiority, endeared by long association: veneration for one’s grandparents, for noble traditions.
4. bias, preference.
5. revere, venerate, consider, admire.
6. heed.