These are the revenue options for redundancy - available to all.
Usually a company making redundancies will have a payroll or tax advisor to ensure they deduct the right tax, and there will be some paperwork for your wife to complete to see what options above to apply - whether she was made redundant & got a lump sum before, whether to waive the pension tax free lump sum (most if not all work pension schemes offer this) in the future. The most important document is the settlement agreement that she should get some independent legal advice on.
The table above is a good way to work out for herself what's the best option tax wise - once updated for her details & circumstance - the years of service, ex-gratia on offer etc. To understand the formulas behind each step - see citizens information or Revenue.ie .
The 'actuarial PV of the lump sum' is a calculation to discount the future value of a pension entitlement into today's money - for example she may be entitled to 34k lump sum @ age 65, with a value today of 12k [random figures to illustrate the point], so 12k would be deducted from the 'Total tax exemption' in options 2 & 4 above. This figure should be provider to her by the employer, and she shouldn't sign the pension waiver document until she gets this amount to see how it affects the overall picture.