The central figure of speech is a trope called a metaphor. This kind of metaphor is an extended metaphor: it is introduced in the first line and has many additional utterances or elements. This extended metaphor might also be called a "conceit" since it calls on extreme and surprising kinds of comparisons. This metaphor implicitly compares a broken down love affair to a broken down old house:
They have taken to patching the floor
While the roof tears.
[The metaphor's comparison of romance to a house is implied because not directly stated as in this metaphor: My love is a red rose (adapted from Robert Burns, "A Red, Red Rose").]
A figure of speech may be one of many techniques that have a non-literal, or figurative, meaning alongside their literal meanings, and their literal meanings often do not make any sense when couched (used) in a figure of speech. For instance, consider this figurative language: The full-blown rose begged to be picked. This is a figure of speech called personification. This personification makes no literal sense because roses cannot literally beg, which is an act that requires overt communication.
Yet figuratively, this personification does make sense. Figuratively, in its non-literal meaning, this statement means the rose was so beautiful that the gardener simply could not resist picking it and having it. Metaphors work the same way. Their literal meanings are senseless, yet their figurative meanings are expressive and, sometimes, revelatory:
They have lived in each other so long
There is little to do there.