How does "rounds" compare to "blocks"? I'm digging for Dogecoins at Hashfaster (Wow! To the moon!), and I'm trying to understand the statistics page. What is the difference between a block (my cpu miner software detects new blocks all the time) and "rounds" (which seems to be some metric on the Hashfaster dashboard)?
A share is a proof of work at the expected difficulty, and can be used in the scope of the pool or of dogecoin.

The difficulty is rather straightforward, if the difficulty goes from 10,000 to 20,000 it becomes twice as difficult to find a block on that network. Pools will accept shares at lower difficulties (say difficulty 1) expecting certain odds on that share being a valid block (in the case of 10,000 difficulty the odds of a difficulty 1 share being a valid block are 10000:1). There are various methods of computing how to pay out rewards for such a share, I will use Bitminter as an example, which like the pool you describe uses rounds to payout, which is referred to as a PPLNSG (Pay Per Last N Groups, or shifts) style pool. 

A round will last until a certain expectation of finding a block is met, with bitminter, when a block is found, you are paid proportionally to your shares against those of others in the pool for the last 10 rounds, with a round duration of 0.4 or 40% of the difficulty. If bitminter was a dogecoin pool and doge difficulty was at 10,000, a round would last 4000 difficulty 1 shares. Whenever a block is found, you will be paid for the amount of difficulty 1 shares you submitted over the last 40,000 submitted in the pool.

The numbers change from pool to pool but hopefully this gives you a little idea on how it works. For more info on other pool payout schemes, check out the top of this article: https://en.bitcoin.it/wiki/Comparison_of_mining_pools