In linguistics, morphology is the study and description of the system of rules and processes of word formation. At the most basic level, words are broken up into "morphemes", traditionally described as "the smallest meaningful units of words".
As an example, a word such as "unhappiness" is a morphologically-complex word composed of at least three morphemes, "un" + "happy" + "ness". (Some linguists argue that the word "happy" is itself morphologically complex, as "hap" may be or may have at one point been a morpheme in English; compare "hapless", etc.)
Productive morphology is the term given to morphemes or other morphological processess which can be freely applied to new (newly-coined, etc.) words in the language. English morphology tends to be extremely systematic, and thus, also extremely productive. For example, the morpheme "-ed", which signifies the simple past tense for many of the verbs in English (tasted, walked, undulated, etc.), is productive; we can coin or create a new verb, and nobody would even think twice about what the simple past tense form of the verb would be. (A perfect example exists here in E2: the verb "ching" and its corresponding past tense form, "chinged".) (Though ryano has now refuted this argument by using the past tense form "chung" on his home node. Drat!)
A problem occurs when, for whatever accident of history, unusual or idiosyncratic word forms exist which differ from the word forms one could reasonably assume would be created via productive morphology. This leads to what are known as "lexical gaps" or "accidental gaps"; word forms that could easily exist due to productive morphological patterns, but that conflict with already established idiosyncratic word forms. Consider the adjectives "concise" and "precise"; the productive morphology for many "-ise" adjectives is that their corresponding noun form is created by adding the morpheme "-ision". ("precise" becomes "precision", etc.) In the case of "concise", though, the corresponding noun form is "conciseness" (although from my observations, "concision" is starting to be used more and more, and is entering the lexicon.)