This formula uses the TEXT function to concatenate the month and year of each date. Then, the two dates are tested for equality. TEXT is a useful function that allows you to convert a number to text in the text format of your choice. In this case the format is the custom date format "myyyy", which translates to: month number without leading zeros & 4-digit year. For example, if A1 contains the date 9-Jun-2015, TEXT(A1,"myyyy") will produce the text string "62016".
Use other cells for input
You don't need to hard-code a date into the rule. To make a more flexible rule, you can use another cells like a variable. For example, if you name cell E2 "date", you can rewrite the formula like so:
Then whenever you change the date in E2, the conditional formatting rule will update instantly. This simplifies the formula and makes it easier to read.
There are several other formulas you could use to solve this problem. For a run-down of 5 different options, see: 5 formulas to highlight dates by month and year