What gives a member of Congress the right to speak freely and be protected on the floor of the Congress?

Congressmen and Congresswomen have the right to speak freely without fear of arrest for the same reasons as all US Citizens - the 1st Amendment to the US Constitution:

"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.