Label Mesh Components 

Components of a mesh can be labeled for illustrative purposes.

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X mesh2d = MeshRegion[{{0, 0}, {1, 0}, {1, 1}, {0, 1}}, Polygon[{{1, 2, 3}, {3, 4, 1}}], MeshCellLabel -> {0 -> "Index"}]

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Labels can be added to an already created mesh using HighlightMesh. Here, the cell index for each edge in the preceding mesh is labeled.

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X HighlightMesh[mesh2d, Labeled[1, "CellIndex"]]

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Labels are not restricted to strings.

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X MeshRegion[{{0, 0}, {1, 0}, {1, 1}, {0, 1}}, {Labeled[ Triangle[{1, 2, 3}], Sqrt[x^2 + y^2]], Labeled[Triangle[{3, 4, 1}], Red]}]

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Label each face of a 2D mesh with its area.

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X SeedRandom[1234]; mr = DelaunayMesh[RandomReal[1, {8, 2}]]; HighlightMesh[mr, Labeled[{2, #}, NumberForm[ PropertyValue[{mr, {2, #}}, MeshCellMeasure], {3, 3}]] & /@ Range[MeshCellCount[mr, 2]]]

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