Editable Grid

You could also use an image field displaying a checkbox.

load(
  local!data: {
    1,2,3
  },
  local!selectedIndex,
  a!gridLayout(
    label: "Editable Grid",
    labelPosition: "ABOVE",
    headerCells: {
      a!gridLayoutHeaderCell(label: ""),
      a!gridLayoutHeaderCell(label: "Data")
    },
    columnConfigs: {
      a!gridLayoutColumnConfig(width: "ICON"),
      a!gridLayoutColumnConfig(width: "DISTRIBUTE")
    },
    rows: a!forEach(
      items: local!data,
      expression: a!gridRowLayout(
        contents: {
          a!imageField(
            images: a!documentImage(
              document: if(
                fv!index = tointeger(local!selectedIndex),
                cons!CHECKBOX_CHECKED,
                cons!CHECKBOX
              ),
              link: a!dynamicLink(
                saveInto: if(
                  tointeger(local!selectedIndex) = fv!index,
                  a!save(
                    target: local!selectedIndex,
                    value: null
                  ),
                  a!save(
                    target: local!selectedIndex,
                    value: fv!index
                  )
                )
              )
            )  
          ),
          a!textField(
            value: fv!item
          )
        }
      )
    )
  )
)

You could also use an image field displaying a checkbox.

load(
  local!data: {
    1,2,3
  },
  local!selectedIndex,
  a!gridLayout(
    label: "Editable Grid",
    labelPosition: "ABOVE",
    headerCells: {
      a!gridLayoutHeaderCell(label: ""),
      a!gridLayoutHeaderCell(label: "Data")
    },
    columnConfigs: {
      a!gridLayoutColumnConfig(width: "ICON"),
      a!gridLayoutColumnConfig(width: "DISTRIBUTE")
    },
    rows: a!forEach(
      items: local!data,
      expression: a!gridRowLayout(
        contents: {
          a!imageField(
            images: a!documentImage(
              document: if(
                fv!index = tointeger(local!selectedIndex),
                cons!CHECKBOX_CHECKED,
                cons!CHECKBOX
              ),
              link: a!dynamicLink(
                saveInto: if(
                  tointeger(local!selectedIndex) = fv!index,
                  a!save(
                    target: local!selectedIndex,
                    value: null
                  ),
                  a!save(
                    target: local!selectedIndex,
                    value: fv!index
                  )
                )
              )
            )  
          ),
          a!textField(
            value: fv!item
          )
        }
      )
    )
  )
)

Using an image field in a grid might impact the overall screen performance as appian has to load the image for every row in the grid. If the grid size grows big then the number of images to be loaded will also grow to hamper the overall user experience.

The best choice for this requirement would be to use the checkbox or radio button as suggested by Tj and parag.