MACRS stands for Modified Accelerated Cost Recovery System and is the most commonly-used tax depreciation method, the other being Section 179 (which technically isn't a depreciation method).
Without getting into too much detail, MACRS is accelerated depreciation that allows for a larger deduction while the asset is still new. By comparison, straight-line depreciation gives you the same deduction year after year over the asset's useful life.
MACRS cannot be used for intangible property, nor can it be used to depreciate:
Films, videotapes, or recordings
Assets put into service prior to 1987 and some types of assets used in 1986
Certain corporate or partnership property acquired in a non-taxable transfer
MACRS convention determines the number of months for which you can claim depreciation during a partial year, either when you first placed the asset in service or when you disposed of it.
The mid-month convention only applies to residential rental property, nonresidential real property, and railroad grading or tunnel bore. It simply means that you get a half month's worth of depreciation no matter when that asset was placed into (or taken from) service during that month, whether that was at the beginning, middle, or end of the month.
The half-year convention works the same way but instead of the month it goes by the year. In other words, you'll get 6 months' depreciation if the asset was placed into service or disposed of during the year, no matter if it was in January or December.
Finally, there's the mid-quarter convention, which can be used for assets that the mid-month convention doesn't apply to, if the total depreciable basis of assets subject to MACRS placed into service during October, November, and December amounts to over 40% of the depreciable basis of all assets (other than residential rental property, nonresidential real property, railroad grading, tunnel bore, and assets that were both placed into service and disposed of during the same year) subject to MACRS that were placed into service during that year. This convention gives you a half-quarter (1.5 months' worth of depreciation) for the quarter in which the asset was either placed into service or disposed of.
Example: you purchased a business vehicle in October, November, or December and that was the only asset you placed into service during the tax year. You'd use the mid-quarter convention for the vehicle. However, if you bought the vehicle in September or an earlier month, you'd go with the half-year convention.