Not a lot else to say on what an appraisal waiver is but I thought I'd add some strategy advise.
In this market appraisal waivers are becoming commonplace. Its important that your agent is able to provide you with a properly prepared CMA so that you know what you are buying is worth what you are paying for it. This at least reduces the risk that you will be having to pay a lot out of pocket to cover a low appraisal. The most important thing with an appraisal waiver is to not do one if you do not have the funds in order to cover it (or are unwilling to assume that risk).
The market is ever changing so there are no guarantees that what you buy today will be worth what you paid for it tomorrow even if the house does appraise. In a multi-family property situation I would be looking more at the cash on cash return, cashflow and condition of the property as an indication of whether the property is a worthwhile investment, if the price I offer doesn't appraise at a bank that shouldn't matter to me if I ran my numbers correctly and plan to hold the investment long-term. Obviously, the better price you get on entry the better the investment will do for you over the long-haul but nobody is giving away multi-families in this market.
If you have a good CMA, and the numbers make sense for you then the last question is whether you have the liquidity to cover the costs of a low appraisal and to what degree. For example if I offer $400,000 for a property with 25% down I have to have $100,000 in cash + closing costs, but lets say it appraises at $375,000 I now need to cover 25% of $375,000 or $93,750 + $25,000 difference of what I offered over appraisal which comes out to $118,750 + closing costs.
When you have an appraisal contingency you have the right to walk away when the property doesn't appraise, or negotiate with the seller if they are willing (maybe meet halfway or they reduce all the way). Waiving that contingency puts you in a weak negotiating position if the property fails to appraise, and also puts your earnest money at risk if you are unable to perform. In a sellers market they can often ask for it because it reduces risk for them, however if a seller receives no offers with an appraisal waiver they will likely accept an offer that does have an appraisal contingency in it.
You can also do a partial appraisal waiver which means you'll waive up to a certain amount. Lets say you only have $15,000 extra cash to put down toward the down payment in the case it doesn't appraise, now you can afford for the property to appraise as low as $380,000 and still go forward with the deal (you'd need $115,000 total in this scenario to go forward with the deal). You submit an offer with a partial appraisal waiver up to the amount you can afford to waive. This makes your offer as strong as possible without putting yourself in a position to lose your earnest money.
Your offer is always a balancing act of indicating to the seller what you are willing and able to do in order to perform, and protecting your earnest money. Every offer is structured differently based on what the buyer can and is willing to do. Just remember not every seller is going to get all cash offers with appraisal waivers, inspection waivers and 3 month leasebacks (even if they are requesting it - if you like the house but are unable or unwilling to do an appraisal waiver it won't hurt you to submit an offer without one, just know your offer is going to be weaker than an equivalent one that has a waiver in it. Worst case scenario is they accept another offer).
Last thing to mention is that less than 8% of properties do not appraise. If you are offering well above asking price or a proper CMA is telling you the property isn't worth what you are paying for it you are significantly increasing your risk of getting a low appraisal. On the other hand if you get a good CMA and it is telling you the house is worth what you are offering you will most likely come out okay on an appraisal or be in a good position to contest a low appraisal.