Conjugations bases are the "true" forms in which Japanese verbs and i-adjectives can be conjugated. They each convey a certain nuance, different from what English verb conjugations mean. Some of these bases can be used by themselves, especially in Old Japanese. In modern Japanese, these bases mostly important for the compound conjugation, which expresses meaning such as tense, mood, attidude of speaker and much more by adding suffixes, verbs and adjectives.
Literally, "ending form", also called predicative form. This is the classical form used in Classical Japanese for ending sentences, hence its name. Dictionaries before Modern Japanese often listed verbs and adjectives under this form. In modern Japanese, this form was replaced by 連体形 (see below) and is only used to make sentences sound more literary/archaic/fancy.
酔(ゑ)ひも為(為) (yoi mo su) Also see illusions. す is the 終止形 of する
Literally, "continuing body form"attributive form. In classical Japanese, it was only used for attributing a sentence to a noun, for example:
人 病気で 死ぬる (終止形) [A human dies of illness.] 病気で 死ぬ 人 (連体形) [A human who dies of illness.]
The first sentence uses the 終止形 to form a simple sentence, the second sentence attributes the sentence "to die of illness" to "human", literally translating to "a 'dying of illness'-human".
Modern Japanese, however, uses this base instead of the 終止形 for ending sentences as well. In modern Japanese dictionaries it verbs and adjectives are thus listed under this form, hence its alternate name "dictionary form".
It should be noted that although the 連体形 is sometimes described as a "base/basic form" or "infinitive form", there is nothing more basic or inifinite to the 連体形 than to other forms. Verbs in Japanese do not have an "infinitive". It is simply convenient to agree on a base when speaking of a verbs plain form.
It is interesting to understand why this base replaced the 終止形:
Firstly, due to the fixed word order when attributing a sentence to a noun and that the verbs always comes last to end sentences, there is no special need to distinguish between a predicative (終止形) and attributive (連体形) form. No confusion can arise. From the viewpoint of convenience and making things uncomplicated, it is reasonable to expect that in normal conversation, this distinction is lost. Indeed, the colloquial language that later became modern Japanese did just this.
Secondly, there may have been more ways of doing this. In the end, common usage agreed on one way:
As a remnant of old Japanese, the 連体形 could also a nominal meaning (used as noun). The particles が originally was quite like の nowadays, linking to nouns. Thus saying, instead of
which uses the 終止形 normally,
人が死ぬ (the dying of a human)
expresses the same meaning within the bounds of classical Japanese grammar. This is also the explanation why が is used to mark the subject in Modern Japanese.
Literally "commanding form". Etymologically, this may simply be a special usage of the 已然形. It is only a small step from saying "as a fact, verb action is completed" to "verb action has to be completed" or "I want verb action to be completed."
This form expresses a very direct command. For 五段活用動詞, this form is used on its own, for 一段活用動詞 the suffixes よ or ろ and others in certain dialects are added to express a command. These suffixes had origninally only an emphatic meaning (do! verb action).
行け!(Go!) 食べろ! (Eat!) 見よ! (Take a look!)