Hayaa itself is derived from the word hayaat which means life.
In English, it may be translated as modesty, shyness, self-respect, bashfulness, shame, honour, etc.
The original meaning of Hayaa according to a believer's nature, refers to a bad and painful feeling accompanied by embarrassment, caused by one's fear of being exposed or censured for some unworthy or indecent conduct.
"Surely Allaah (is One who) has hayaa and is the Protector. He loves hayaa and people who cover each others faults." Saheeh al-Bukhaaree
"Every way of life has a innate character. The character of Islaam is hayaa." Abu Daawood
"Hayaa does not bring anything except good." al-Bukhaaree
"Hayaa comes from eeman; eeman leads to Paradise. Obscenity comes from antipathy; and antipathy leads to the fire." al-Bukhaaree
"Hayaa and Trustworthiness will be the first to go from this world; therefore keep asking Allaah for them." al-Bayhaaqee
"Say to the believing men that they should lower their gaze and guard their modesty: that will make for greater purity for them: and Allaah is well acquainted with all that they do. And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what (must ordinarily) appear thereof; that they should draw their veils over their bosoms and not display their beauty..." [Soorah an-Noor (24):30-31]