General:
* Be logical
* Be coherent
* Be understandable
* Be clear
* Be reasonable
* Be rational
* Be plausible
* Be credible
* Be comprehensible
* Be intelligible
* Be cogent
More specific:
* Follow: "This plan follows" (implies logical progression)
* Add up: "Her story doesn't add up" (implies consistency)
* Hang together: "The evidence hangs together" (implies interconnectivity)
* Hold water: "His alibi doesn't hold water" (implies soundness)
* Track: "I can't track his reasoning" (implies ability to follow)
Informal:
* Cut the mustard: "His excuse doesn't cut the mustard"
* Click: "It all clicked when I finally understood the instructions"
* Ring true: "Her story rang true" (implies authenticity)
* Make a lick of sense: "It doesn't make a lick of sense!" (implies complete lack of understanding)
The best synonym to use depends on the context and the desired level of formality.