Caius is the assumed name of the Earl of Kent, Lear's most loyal and devoted servant. Kent is a wise, decent man, a man of great integrity. When Lear makes the foolish mistake of banishing Cordelia from his kingdom, Kent tries to intercede on her behalf, only to suffer the same fate. Despite this shabby treatment, Kent still wants nothing more in life than to serve his king. Only he can't do this as the banished Earl of Kent. So he disguises himself as a servant called Caius to be close once more to his beloved master.
Kent always was a servant of the king, to be sure, but in a much more exalted capacity. His lowlier state in life mirrors that of Lear himself. Just as Lear has come down in the world, so has the Earl of Kent (Caius). This shows us how seriously Kent takes his loyalty; he served his master during the good times, and he'll gladly do so now that times are bad. Kent loves his king dearly, and disguising himself as a humble servant shows that he accepts that his fate is inextricably bound to Lear, come what may.