On many mining pools/bonds I see things listed as 105% PPS / 110% PPS weekly payout. What does PPS actually mean?
Where I've seen it, it refers to the mining payment method "Pay per share".
This question has an answer that describes what a "share" is.
On some mining sites that have existed, the earnings for a share have been essentially paid immediately. However, this method exposes the pool operator to a possibility of loss in the case that, on average, they find less that the expected number of blocks. This can be made much worse by a large miner participating in the pool and performing a block-withholding-attack. To prevent these problems, most pool operators prefer slightly modified pay-per-share methods of payment, such as SMPPS (Shared Maximum Pay Per Share).
A payment method is not strictly Pay Per Share if the earnings aren't available for payout immediately, or if risk is passed on to the miner. Note also that it may not always be clear how much of a fee is being charged by a pool operator; it can be as low as 0% or as high as 7% (but if they tell you the payment per share, you should be able to work it out by dividing the block reward of 50BTC by the current difficulty and comparing it with what the pool pays).
A pool would not payout 105% or 110% except perhaps as a promotion when it is trying to increase its number of participants and offers an increased reward such as 55BTC per block (ie 110% of what is earned) at its own cost.
Update: The discussion you linked to in your comment is regarding the issue of mining "bonds" where the issuer promises to pay 110% of the shares mined. Each bond appears to be selling for around 0.6BTC, and represents 2Mh/s of mining speed. Given that the bonds are "perpetual", presumably the issuer has allowed for equipment replacement and maintenance costs, and power etc. Payouts are advertised as "currently 110% of PPS", so it is presumably a promotional offer. The issuer must be earning a margin somewhere along the way to cover the cost.
PPS is "pay per share", a mining pool reward system where the operator gives a set payment per share submitted proportional to its average worth, regardless of how many valid blocks the pool finds. This way the miner doesn't suffer any variance.
By extension, 100% PPS is the reward that would have been given for a certain hashrate at a PPS pool without a fee. 110% PPS is 110% this amount, etc.
Some pools, for example Chaang-Noi's project, are really pool-hopping proxies so they are able to offer >100% PPS to miners. Things like merged mining, preference for newly generated coins, attacks on Bitcoin or alternative currencies or using the hashrate for things unrelated to Bitcoin - or proxying to gpumax.com, which itself is based on any of the above - can also allow a pool to offer >100% profitably. It could also be a promotional offer.
Some mining bonds state that they pay >100% PPS as a marketing gimmick.