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Cardi + o + logy needs a bridge — say "cardilogy" out loud and hear why. Greek and Latin
word-parts almost never end and begin with vowels that sit naturally together, so a linking vowel gets dropped
in purely to keep the word pronounceable.
It's not decoration. Pull it out and the word collides into an unpronounceable cluster;
put it in, and two solid word-parts click together cleanly — the same job as the space between two spoken words,
just glued in instead of left open. O is the most common one in medical terms,
i shows up occasionally, and e is rarer still — genuine, but really only in
one family of words.
See it at work
GynecologyGynec + o + logy
CalcificationCalc + i + ficat + ion
CholelithiasisChol + e + lithiasis