Phonemes are perceptual categories. Whatever actual phonetic form they take, we perceive them as part of category X.
Phones are just sounds. "Gradient" means somewhat variable. So an individual instance of a sound is not gradient. It's just some precise acoustic/articulatory information. But in general a phone like /t/ is gradient because no two sounds are identical. Phonemes, however, are also gradient in a sense: they're categories that contain infinitely many subtle variations in pronunciation, still within the same category.
Phonemes are perceptual categories.
Phones are analytical categories used by linguists (and perhaps orthographers).
Phonemes are phones (fewer phoneme categories, more phone categories). Allophones are subphonemic variations in phones-- not perceived to be different, but different enough for the analyst to note it.
Think of phonemes as geometric shapes you recognize ("triangle"). Think of phones as shapes relevant to mathematicians ("acute triangle"). And think of gradience/variation as the real-world instances of those shapes in general (perhaps a "yield" sign). (Allophones then would be variation in context, so perhaps different sizes of street sign depending on the distance from which observers were looking.)