I signed up to the site, and started mining, but I don't quite understand how doing so is going to accelerate my earnings. Surely with such a claim as this there should be more 'splaining going on, and since I'm not very technically minded I wouldn't understand techy talk.
Absolutely. Your earnings will be accelerated in three specific ways with Triple Mining.
1: Low 1% fee. Most mining pools charge a 2% fee or greater, so you're immediately ahead of the game. 99% of the found block goes to pay the workers proportionally to their efforts.
2: Jackpots. Until July 8th, there is a random .5BTC jackpot given away to a random miner (regardless of hash rate) every single day. After that, a percentage of that 1% mentioned above will be set aside into a special jackpot area, to be awarded once a week along with the find of a block to a random miner in the pool. The larger the pool, the larger the jackpot.
3: Minipools. This means that for everyone you invite to mine with you you'll get their 1% fee as long as you're mining as well. If you invite 5 friends with comparable hash rates, this means that instead of a 1% fee really you're getting a 4% bonus on top of no fees. ie: if you'd usually make 3BTC/week, you'll instead make 3.12BTC/week. With other pools you'd instead make closer to 2.91BTC/week. It may seem like a small change, but it definitely adds up. Why make less than you could be making?
Sounds like you get smaller payouts. On average, you will get money in a pool before solo mining, but the payout is split. If you are solo mining, you may be waiting a long time and never get a payout if the difficulty rises.
In general, this is the idea behind mining pools. With Triple Mining, however, the fee is extremely low and basically gone after you invite a single friend to mine with you. With the larger mining pools, I've gotten regular payouts averaging about .008 BTC. This can be nice to track your progress, but its not nearly as fun as getting a full BTC every day or two when a smaller pool solves a block. I sincerely feel that Triple Mining both will increase your earnings beyond any other mining pool and solo mining, and will be a lot more fun with the larger 'chunk' earnings you receive rather than pennies here and there.