An expunction is the best way to completely erase from your criminal record, the fact that you were ever arrested, accused of or charged with an offense. To be eligible for an expunction your case must have been DISMISSED without a conviction or guilty plea.
If you plead guilty to your offense and completed a deferred adjudication probation, you are probably not eligible for an expunction but you may be eligible for an order of nondisclosure, which seals records of the offense for most purposes, but they would not be hidden from official licensing agencies, (if for example you are applying to be a nurse or a doctor), and it would not hide from prosecutors the fact the offense occurred in the event that you ever pick up a 2nd case of the same offense (for example a DWI 2nd).

If you were convicted of an offense, served a regular probation or did time in jail or prison, then that offense is not eligible to be sealed or erased from your record.