Simply put, "chattel" is personal property. It can also be thought of as movable property in contrast to immobile property - the land and the buildings (i.e. the house itself). Chattel in your real estate investments includes things like appliances (stoves, refrigerators, dishwashers, clothes washer/dryers, etc), curtains and window blinds, furniture you own as the owner of the property (vs. that owned by the tenant), carpets not permanently attached (not glued down), etc.
The reason chattel is important to real estate investors is that these items have shorter depreciation schedules than the real property they're a part of. Whereas residential rental property (the structure) has a 27.5 year depreciation life, chattel items might have a depreciation schedule of only five years. This allows us to accelerate the amount of time it takes to expense these items off our income vs. simply depreciating them as part of the structure as a whole.
As an example let's say we purchase an investment property with a depreciable value of $100,000. Using a normal 27.5 year schedule, each year we get to deduct approximately $3600 in depreciation expense from our rental income. If, however, we had a chattel appraisal done and determined that $25,000 of this $100,000 value consisted of chattel with a five year depreciation life our total depreciation for each of the first five years could be increased substantially. Instead of $18,000 in total depreciation deductions over the first five years of ownership ($3600 x 5) we would have approximately $38,500 we could write off ($25,000 in chattel plus $2700 per year on the remaining $75,000 value of the structure) - a $20,500 difference!
This is a very simple example and comes with some significant caveats. The intent is simply to get the idea across. It should also be noted that in the example above the remaining years (after the first five) will only have approximately $2700 in depreciation expense available for deduction from our rental income each year. That's really part of the idea, though, to "accelerate" some of that depreciation deduction to the first years we own the rental property.
Having a chattel appraisal or cost segregation done on a small residential rental property may not pay off in the long run. Expensing chattel separately from the rest of the property is a valid concept however and is worth thinking about. One respected company that offers services related to chattel on residential rentals is Marshall and Swift. You can learn more at their website taxsegexpress.com.