Rime is a type of ice that forms when the moisture in fog freezes suddenly on an object. The white frost that forms on trees along mountain ridges is rime.
Rime can cause trouble for aircraft, as it also forms when a cloud's water droplets freeze to a surface, like the metal body of an airplane. Another, completely different, meaning of this word is "rhyme." It's simply an old-fashioned way to refer to the ending sounds of two words that sound alike — like "mouse" and "house." And "The Rime of the Ancient Mariner" is just a very long, very old, rhyming poem.