Also spelled phonestheme.
A phonaestheme is a cluster of phonemes which tend to give words that contain them a similar meaning. A good example of an English phonaestheme is "sn-" which has the meaning of "nose", as in:
"snot", "sniff", "sniffle", "sneeze", "snicker", "snigger", "sneer", "snout", "snarl", "snort", "snivel", "snore", "snuff", "snuffle", "snorkel", (and with the postalveolar varient "schn-") "schnoz", "schnozzle", "schnorkel", and "schnauzer".
Phonaesthesia is not the same as onomatopoeia, because in onomatopoeia the entire word is designed to sound like what it represents, while in phonaesthesia it's only a small part of the word and it doesn't really sound like anything. "Achoo" is an onomatopoeia; the "sn-" in "sneeze" is a phonaestheme. Phonaesthesia is also different from morphemics in that all instances of a morpheme have the same etymon but words with the same phonaestheme often have different etymological derivations.
Phonaesthemes don't have to be consonant clusters. An example of a vowel phonaestheme is how words for small things often contain closed, high vowels:
"teeny-weeny", "itsy-bitsy", "mini", "little", "bit", "kid", "eek"...
Of course a counterexample would be "big" and "small", so that just shows you how reliable phonaesthemes are.