A back-formation is a new word produced by excising an affix, such as producing the verb secrete from the noun secretion. Many back-formations, like that one, acquire respectability, but others, especially more recent coinages, are considered nonstandard, so use them with caution.
Back-formation can be seen as a form of clipping, though the distinction between one category and the other is that clipped forms (ad in place of advertisement, for example) are the same part of speech as the original form, whereas most back-formations are verbs formed from nouns. (Many back-formations are formed from words ending in -tion, such as automate and deconstruct.)
Most back-formations eventually take their place among other standard terms, though they are often initially met with skepticism. For example, curate and donate, now accepted without question (and associated with the high pursuits of art and philanthropy, respectively), were once considered abominations.
Newer back-formations that careful writers are wise to avoid include attrit, conversate, enthuse, incent, liaise, spectate, and surveil. These buzzwords are convenient — hence their creation — but they are widely considered inelegant, and in the case of at least a couple of them, concise synonyms are already available. (To spectate is to watch, and to surveil is to observe.)
Sometimes, a back-formation is derived from a noun describing an action, as with attendee from attendance, or from a noun describing an actor, as with mentee from mentor. Many people consider such terms aberrant, and they are also ill advised in formal writing.
Other back-formations derive from confusion about a base word. Cherry and pea both developed from the assumption that the original terms cherise and pease are plurals. More recently, biceps (and triceps) and kudos have been misunderstood as plurals, resulting in bicep, tricep, and kudo. Although cherry and pea were accepted without reservations into English long ago, bicep, tricep, and kudo are still considered nonstandard.
Another class of back-formations are those shorn of their prefixes for humorous effect, such as gruntled from disgruntled and kempt from unkempt; rarely do such truncations enter the general lexicon.