If you have a homeowners policy, you should have "contents" coverage, which generally means all your stuff-- your t.v., furniture, pots and pans, clothes, handbags, etc. Most homeowners policies automatically cover your contents for 40%-75% of what your home is insured for (depending on your carrier.) For example, if your policy goes with the 75%, and your home (your dwelling) is insured for $200,000, your contents will be given a blanketed value of $150,000. Most of the time, they will pay out the actual cash value of your contents, which is the replacement cost minus depreciation. Some carriers offer the replacement cost option for extra premium. If there's a fire and your handbags are ruined, they will want you to produce documentation/receipts/invoices to show how much your items cost. If you're looking for better coverage for your handbags, jewelery, or other high valued items, ask your agent for endorsements or floater policies that will pay out the replacement cost of those items-- not their depreciated value. They'll ask you to create a schedule, or an itemized list of your stuff, with serial #s, receipts, and/or appraisals (if you have them.)
Renters policies also offer coverage for your contents, but you can pretty much choose whatever limit you want. It isn't based off a percentage of your home because you aren't insuring the home. It will give you liability coverage (for when a neighbor accidentally slips and falls in your living room which isn't your fault, but the law says it's your fault... LOL) and contents coverage (for your stuff.) They also usually include some medical payments coverage, property of others coverage, and additional living expenses coverage. Renters policies are a very smart thing to have!
I hope that wasn't too confusing.