Definition: Kalispera is a common greeting used in the afternoon and evening in Greece. You'll hear it from taverna touters, friends, and older Greeks taking a "volta" or evening walk around the plateia or plaka, or town square. It's usually translated as "Good evening", but it starts being used well before dusk, in the later afternoon. Kalispera sas is a more formal greeting, used by the polite to elders, guests, or persons deserving of respect.
Kalispera by itself generally is just another way of saying "Hi! Please come on in and sit down on one of the chairs at my taverna and order your big evening meal!" You can return the phrase by simply saying "Kalispera!" right back, without further obligating yourself to join them for a meal.
Breaking it down, the actual word combines kali or "good" "beautiful" with "spera" or hope and actually means something close to "Good hope" or "Best wishes", but it is never translated this way, any more than the English "Goodbye" is translated as "God be with you", though that is the origin of that phrase. It is a kind of casual blessing for the coming night, when everyone must sleep.
"Kali oneiros" is another phrase that is used only at night, and it means "good dreams", once again using the word "kali" for good or beautiful, and combining it with oneiros, the ancient (and pre-Greek) word for dreams.
Common Misspellings: kalespera, calispera
Greek Letters: Καλησπέρα
Other similar greetings starting with a "Kali" sound include kalimera (Good morning!), kalinikta (Good night!) and kalomena (Happy First of the Month - any month). If you've forgotten the right ending for your greeting, you may be able to get away in almost any greeting situation with a clearly spoken "kali" followed by a muffled second word.
The forgiving Greeks, who love any attempt at using their language and who will always give the poor Greekless foreigner the benefit of any doubt, will still smile encouragingly and pretend that you (almost) got it right.
Interested in learning more Greek? Here's a quick and easy way to Learn the Greek Alphabet. I recommend learning the fundamentals of the Greek alphabet as it can ease your travels in many ways, from reading road signs and airport or train schedules to figuring out where you are based on corner street signs, which are usually only in Greek letters. Highway signs usually are in both English-style lettering and Greek letters - but the Greek ones come up first on the road, giving you extra time to make that upcoming turn if you can tell what they say earlier rather than later.