"Der/Dieser Mai ist perfekt." is mostly used. For example when you chat with someone about this month, where the sun shines so beautifully and you can play most of the time outside. “Mai ist perfekt.” is very rarely used (if at all).
This is also valid, when you speak of particular other time: “Das/Dieses Wochenende ist perfekt/ schön/ langweilig/ katastrophal.” “Die/Diese Ferien sind…“ „Der/Dieser Tag ist…“
A link for more information about dieser/ diese/ dieses: http://www.canoo.net/services/OnlineGrammar/InflectionRules/FRegeln-P/Pron-dieser-jener3.html
I don't think it's a phrase of some kind. It's just a rather complicated grammar of German, that nouns - in most cases - are preceded with their article. all months names are masculine names; hence, "der Mai". However, in a sentence like 'Es ist Mai.' the article is not needed. It would be nice if someone could expand on this.
The purpose of the words, "the" and "a" as definite articles are to show how unique or specific a noun is. If there is one dog in particular you're talking about you say "the dog". This shows that this particular dog is relevant to the conversation. I believe German takes it a step farther, since there is strictly, one May, putting "der" shows how specific it is, since May is a fixed point, there won't ever be a point when there's multiple mays in a year. An example that we have in English would be like saying, "The day has been great so far". Since we know that this day is specific, we say "The Day" labeling it in a sense. I'm not good at explaining things, but I'll try to help you the best possible, just reply. ;)
As someone above said, the context you'd use "Der Mai ist perfekt" would probably be when trying do decide on a date, for example: Paul: Im April habe ich leider keine Zeit dich zu besuchen, wie wärs mit Mai ("Unfortunately, I don't have time to visit you in april, how about may?") Linda: Der Mai ist perfekt! ("May is perfect!")
I guess it would be grammatically incorrect to just say "Mai ist perfekt" without the article. Remember, you can't keep comparing English to German because at the end of the day, they are two different languages with completely different language rules for the most part. My German teacher always asks us to leave our English at the door before coming in and I think that really helps :) leave your English at the log in!