When the sheriff shows up with the eviction notice, he lets the tenant know, by leaving the notice, to expect law enforcement officers to show up on a set day to physically evict the tenant if he has not abandoned the property yet. Eviction is certain at this point.
By the time the sheriff shows up, the eviction process has almost run its entire course. The process begins when the landlord provides the tenant with written notice. This has several different forms: the "Pay Rent or Quit" notice, the "Cure of Quit" notice, or the "Unconditional Quit" notice. The first type happens when the rent is late, the second type happens when the tenant has violated the lease in some other way, such as having unauthorized pets, smoking on the property or making too much noise, and the third is usually the result of multiple violations. The first two give the tenant a remedy to solve the problem, while the third does not.
After the notice, if the tenant does not remedy the situation, a court hearing occurs. Defenses against eviction are quite rare, and the judgment that comes set the stage for the sheriff delivering the final notice. In some states, even if the tenant leaves at this time, if he leaves his belongings, the landlord must follow rules for storage and notification before getting rid of them. Knowing state law about evictions and tenants' rights is crucial at this point for both the landlord and tenant.