An eviction is a judicial process where a tenant is removed from their home for failing to abide by their lease (e.g., non-payment of rent, holding over the lease term, criminal activity, etc.). You cannot be legally removed from your home until a judge orders an eviction.
To begin the process, the landlord is required to give you a "notice to vacate" that says you have 3 days to vacate the premises (it could be shorter or longer than 3 days if your lease provides for a different time frame). Once the 3 days expires, only after that can the landlord file a lawsuit for eviction (called a forcible detainer) in the Justice of the Peace court.
The court will then set your case for a hearing. If you lose at the hearing, you have 5 days to appeal to the county court at law. If you do not file an appeal, the court may issue the "writ of possession" after your appeal period has expired. A writ of possession is the document authorizing the landlord to remove you with the Constable's assistance. Once the writ of possession is issued, the Constable will post a 24 hour notice of removal at your residence. The next day the landlord and the Constable will come and forcibly remove you and your property from your home.
Note that in the City of Dallas, landlords are required to give a COVID Notice of Proposed Eviction prior to providing a notice to vacate. The notice gives the tenant 21 days to respond in writing to the landlord alleging a COVID-related reason for falling behind on rent. If you respond, you will have a full 60 days from the date the notice of proposed eviction is given before the landlord may give you a notice to vacate.