We hope the "Holy Grail" part is pretty self-explanatory: it's what they're after, the reason for the season, the object of the quest. The Holy Grail is a staple of Arthurian lore; it's the cup that Jesus is said to have drunk from at The Last Supper/the cup that caught Jesus' blood when He was crucified. It's usually portrayed as a golden, glowing cup or chalice. (Although we know better—we've seen Indiana Jones and the Last Crusade and The DaVinci Code.) We could continue with all the historical what's-what, but let's just say it's important and sacred and get on with the interesting part: Monty Python.
For starters, it's the name of the comedy group, first made famous by their sketch TV show Monty Python's Flying Circus; but where does "Monty Python" come from? Apparently it comes from… nowhere.
Here's a quick interview with Palin, where he describes the creative process as coming up with random names that made them laugh. There's some speculation that Monty refers to Lord Montgomery and even a story of Monty being a regular at a bar Cleese frequented. At any rate, it's really about the silliness of the name rather than any sort of deeper meaning or significance that people like to think it possesses—it has a totally opposite connotation to the "holy grail."
Including the Monty Python name in the title made sure that no one would mistake this film for a serious piece of Arthurian fiction. It signaled a total sendup up of anything sacred or serious.