Incoherent thoughts don't follow each other logically. Incoherent speech is mumbled or jumbled. Incoherent means that something is difficult to understand because it's not holding together.

A lot of people use incoherent to mean unintelligible, which is a perfectly fine usage. But it specifically means unintelligible due to a lack of cohesion, or sticking together. An incoherent argument may sound something like this. "I deserve to go to the dance because it is the second Tuesday of the month and my feet are a size ten." The reasons do not follow each other logically and do not even relate. It's an incoherent mess.

Definitions of incoherent
  1. adjective
    without logical or meaningful connection
    “a turgid incoherent presentation”
    confused, disconnected, disjointed, disordered, garbled, illogical, scattered, unconnected
    lacking orderly continuity
    confused and not coherent; not clearly thought out
    illogical, unlogical
    lacking in correct logical relation
    not consistent with or using reason
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    coherent, consistent, logical, ordered
    marked by an orderly, logical, and aesthetically consistent relation of parts
    perfectly consistent and coherent
    capable of or reflecting the capability for correct and valid reasoning
    consistent with or based on or using reason
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  2. adjective
    unable to express yourself clearly or fluently
    incoherent with grief”
    synonyms: tongue-tied
    inarticulate, unarticulate
    without or deprived of the use of speech or words
  3. adjective
    (physics) of waves having no stable definite or stable phase relation
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    (physics) of waves having a constant phase relation
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