A tax sale occurs when the owner of the property has failed to make his ad valorem, or property tax payments. In Texas, the length of time a county will allow taxes to remain unpaid before beginning the foreclosure process varies from county to county, and in many instances, will vary within the county. The taxing authority must file suit for taxes due and then advertise the property for sale. If the property owner still fails to to bring the delinquent payments current, and pay the statutory penalties, the property goes up for auction at the courthouse between legal hours on the first Tuesday of the month. The bid typically starts at the amount of the unpaid taxes plus penalties.
To the second part of your question, if you are the winning bidder at the tax sale, the deed to the property is conveyed to you via a tax deed. The tax deed provides for conveyance of all the rights and interest the former owner had at the time when the tax assessment was made, so you now own the property. The deed also specifically provides for the redemption period and penalties. The redemption period gives the original debtor the right to buy back his property from you if he pays the statutory penalties, and delinquent taxes. He has two years to exercise his right of redemption, with penalties increasing the longer he waits. After that period of time, there is not any other recourse afforded the debtor, and the property becomes yours without encumberance.