Without a suffix:

連用形 forms participles “-ing,” and is also the form used to form a compound verb; for Quasi-Adjectives (nari, tari), it forms adverbs (ni, to).

終止形 acts as a main verb.

連体形 makes a verb a noun modifier, and also acts as a main verb (after ぞ,かな,か,や).

已然形 acts as main verb after こそ.

命令形 expresses a command.

For the sake of space, the conjugations have been abbreviated in the notes to each poem as follows:
Classes: 上 = 上二; 下 = 下二; 特 = 特別
Endings: 未 = 未然形; 用 = 連用形; 終 = 終止形; 体 = 連体形; 已 = 已然形; 命 = 命令形
to yield the following abbreviated table of Classes and Endings:

So, for example, from Poem #1: [(ぬる wet 下用)(つつ Continuative)] indicates that the verb ぬる means ‘to wet,’ and that it is of the 下二 Conjugation, with the 連用 Ending. This Ending is required in order to attach the Suffix -つつ, which means ‘Continuation.’ つつ is indeclinable (never changes shape).

Hence the whole verb phrase means – ‘keeps on getting wet.’