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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, but i, e, and a all pull the same duty elsewhere.
See it at work
GynecologyGynec + o + logy
PneumomediastinumPneumo + medi + a + stinum
Spina BifidaSpin + a + Bi + fid + a