This is the clamp that connects the battery cable to your battery. On Honda (Civic, Accord, CR-V, Fit, City), it causes a lot of "no start" problems.
Signs of bad / loose battery terminal:
• Car won't start in morning, just "click click" sound
• Dashboard lights flicker on and off
• Everything goes dead then comes back when you shake terminal
• White / green powder on terminal (corrosion)
• Car cuts off when you hit pothole or bump
• Radio and clock resetting every time
Very common on Honda because the original terminals are soft lead and they expand.