For trips not to the Berlin area (public transportation areas ABC and counties adjacent to Berlin), a lump sum for meals and other extra costs is paid in most cases. For trips within Germany, that is currently (2018) 12€ each for the days travelling there and back, and 24€ a day for each full day spent on business travel. This lump sum is intended as a compensation for extra costs occurring while away on business.
The amounts that are reimbursed for trips outside of Germany can be found in the ARVVwV, for 2018 here.
If meals are being provided for free or are, for example, included in the hotel cost, the lump sum is being reduced by 20% of sum for a whole day for breakfasts and by 40% for lunches and dinners.