"Conueries" is a term DreamHost came up with to measure MySQL database usage. The word is a combination of "connections" and "queries", as that is what the unit is derived from. Basically, the number of MySQL queries you have in a month, plus 25 times the number of connections you have is your total "conueries" for a month.
As of August 2015, conueries are no longer visible in the panel.
You can still access your MySQL usage page at the following link:
They are no hard limits on conueries. DreamHost still tracks them, but unless you're in the top .01% of database users, you'll never need to worry about them again. DreamHost reserves the right to have ultra-heavy users curtail their database usage or switch to a Dedicated server. However this would only be an issue with an extremely inefficient site receiving thousands of visitors a day.