The mid-month convention states that, no matter when you purchase a fixed asset in a month, you assume that it was purchased in the middle of the month for depreciation purposes. Thus, if you bought a fixed asset on January 5th, the convention states that you bought it on January 15th; or, if you bought it on January 28, you should still assume that you bought it on January 15th. By doing so, you can more easily calculate a standard half-month of depreciation for that first month of ownership.
If you choose to use the mid-month convention, this also means that you should record a half-month of depreciation for the last month of the asset's useful life. By doing so, the two-half month depreciation calculations equal one full month of depreciation.
Many companies prefer to use full-month depreciation in the first month of ownership, irrespective of the actual date of purchase within the month, so that they can slightly accelerate their recognition of depreciation; doing so reduces their taxable income. Also, the mid-month convention introduces some complexity to the calculation of depreciation, making it more likely that a calculation error will occur.