Though the acquisition of renters' insurance is ultimately your tenants' responsibility, as a landlord it's important that you have an understanding of what it is and why it's important, both for your own well-being and for your tenants'.
Make Tenants Aware
Your tenants should be aware that in the case of a destructive event at your property (fire, natural disaster, theft, etc.), existing property insurance will only protect your actual property. In other words, tenants' possessions and personal belongings are not covered.
Your Benefit
Some property managers build a clause into their lease stating that renters are obligated to purchase renters' insurance for the duration of their occupancy. In cases where a tenant without renters' insurance is sued by a third party who is injured in their apartment, you can be included in the lawsuit and are not covered if the tenant does not carry insurance.
Tenants' Responsibility
If you choose not to include renters' insurance as a lease requirement, you should still make a point of informing renters that they are responsible for insuring their own personal belongings, both verbally upon lease signing and in the actual lease text.