A value is any of the possible levels of variability that a variable may achieve.
For example, the variable "temperature" may have values measured in degrees of heat, such as 0o, 1o, 2o, etc, inlcuding negative values such as -1o, -2o, etc. On occasions, you may need smaller, more precise, values, such as 1.12o, 1.13o, 1.14o; other times, you may well do with larger values, like categories, such as 0-9o, 10-19o, and so on. Also, depending on the scale used, the degrees may refer to Fahrenheit or Celsius. Of course, other possible values for heat may be categorical, like "very cold", "cold", "mild", etc.
Some researchers, however, use the concept value to refer only to the numerical expression of levels of variability, and, instead, use the concept attribute to refer to the verbal expression of such levels of variability.
For example, the variable "gender" would have two attributes: male and female (or men and woman, or boy and girl). These attributes would be considered as values whenever the attributes are expressed numerically. Thus, male or female are variable attributes, while 1 (for male) and 2 (for female) are possible (numerical) values used to represent those attributes in a data set.