What does "INFINITE resistance" in a circuit mean?

When R = infinity Mohms, Does this mean that the circuit has NO current? Does this mean that the circuit is OPEN? Does it happen when the circuit is not connected properly? Does it happen when the circuit is completely grounded? Where does this phenomena, of R = infinity, happen? jfyi... I used a relay... show more When R = infinity Mohms,

Does this mean that the circuit has NO current? Does this mean that the circuit is OPEN? Does it happen when the circuit is not connected properly? Does it happen when the circuit is completely grounded? Where does this phenomena, of R = infinity, happen?

jfyi... I used a relay switch in a circuit and observed infinite Resitance on a multimeter during one position of the switching operation... now I am trying to figure it out! Thanks for reading even if you can't help.
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