It seems that the Jacobian ratio is defined as the ratio between the maximum and minimum Jacobian determinant in an element [1, 2]. And, that a value between 0.33333 and 1 is good-enough .
Nevertheless, for linear elements, the Jacobian is constant and thus the same over each element. As mentioned by @GustavoCosta, 3 descriptors commonly used for element quality check are aspect Ratio, internal angles, and Jacobian determinant. But there are many more as mentioned in a previous answer and references there. You might also want to check reference 4.
Kwok, W., & Chen, Z. (2000, October). A Simple and Effective Mesh Quality Metric for Hexahedral and Wedge Elements. In IMR (pp. 325-333).
Bi, Z. (2017). Finite Element Analysis Applications: A Systematic and Practical Approach. Academic Press.
Bucki, M., Lobos, C., Payan, Y., & Hitschfeld, N. (2011). Jacobian-based repair method for finite element meshes after registration. Engineering with Computers, 27(3), 285-297.
Shewchuk, J. R. (2002). What is a good linear finite element? interpolation, conditioning, anisotropy, and quality measures (preprint). University of California at Berkeley, 73, 137.