My company requires "verified test equipment" to have a "described verification process".
From this wording I understand that the requirement is internal, i.e. doesn't originate from regulation, a published standard etc. As such, and in the absence of additional guidance, you are free to interpret it literally. "Verification" means provision of objective evidence that specified requirements have been met. So first, the measurement equipment item needs to have documented and approved performance requirements. What actions you need to take to be able to provide objective evidence that these requirements have been met depends on what the requirements are.
"Described verification process" (assuming verbatim quoting) is a poor wording, because description may be verbal... The intent was more likely "documented verification process". This is still a little ambiguous because it doesn't clarify whether a standard procedure for this activity needs to exist, or would a retroactive documented report suffice (i.e. a report describing what has been done and the results obtained, providing objective evidence that the specified requirements have been met).
Only going to be used in analysis for checking parts, but not advising changes to the parts so they say it doesn't need to be calibrated.
Unsure who "they" are, whether "say" refers to verbal expressions or to some binding document, and what the basis of this determination is.
Generally speaking, and in the literal sense, "Calibrate" means, in this context:
Correlate the readings of (an instrument) with those of a standard in order to check the instrument's accuracy. (Oxford Dictionary)