na-adjective
Almost exclusively used in the set phrase つぶらな瞳 (round, cute eyes). Describes eyes that are large, round, and endearing.
彼女のつぶらな瞳が印象的だった。
Her round, cute eyes were striking.
子犬のつぶらな瞳に見つめられると、つい甘やかしてしまう。
When the puppy looks at me with its round, cute eyes, I can't help but spoil it.
丸い simply means 'round' or 'circular' and can describe any round object. つぶら is specifically used for eyes and carries a nuance of cuteness and charm.
The origin is uncertain. It may be related to 円 (つぶ) meaning 'round', but the exact derivation is unclear.