What is a Accelerated Rent?

If a tenant defaults on a lease (e.g., failure to pay rent on time, damage to the premises, keeping a pet when it is not part of the lease, etc. ) then the lessor can evict the tenant. At that point, the lessor can demand the full balance of the lease be paid immediately.

Enforceability varies from state to state. You should see a lawyer specializing in landlord/tenant law if you are caught in this situation.

Avoid any lease that has what appears to be an "Acceleration" clause.