calendar with today function

TODAY() returns a date already. You don't need to nest it in a DATE() function. The formula should be

DateTable = CALENDAR(
	DATE(2015; 6; 1);
	TODAY()
)

I recommend naming your calendar table "DateTable" instead of "Calendar". The word Calendar is reserved for the function named CALENDAR(), so every time you refer to that table you would have to put its name in single quotes. I find typing extra quotes around my table names annoying and try to avoid it wherever possible.

So you would be able to type

Measure = CALCULATE( [MeasureName], DATESYTD(DateTable[Date]))

instead of

Measure = CALCULATE( [MeasureName], DATESYTD('Calendar'[Date]))

because

Measure = CALCULATE( [MeasureName], DATESYTD(Calendar[Date]))

would return an error.

The purpose of the DATE() function is to construct dates from components. It requires 3 separate arguments: a year, a month, and a day, each in the form of a whole number, and from that it returns a single item as its output: a full date. TODAY() takes no arguments, and also returns a single item: a full date. So TODAY() when nested in another function only constitutes one argument, not three, and also it doesn't fit the requirements of any of the three arguments needed for DATE(). It isn't a year, it isn't a month, and it isn't a day. It's a full date.