Abarim Publications' online Biblical Greek Dictionary
The feminine noun πετρα (petra) means rock or rather: mountain of a rock, and is used 16 times in the New Testament; see full concordance. A much more common Greek word for stone is τιθος (lithos), which tends to denote a worked stone, whereas πετρα (petra) tends to denote a naturally occurring rock.
A Hebrew counterpart of our noun πετρα (petra) is the noun צור (sur), from which comes the name Tyre, the capital of Phoenicia. It is, of course, highly significant that Solomon's temple was in a very large part Phoenician; one might say that Solomon built his temple upon that Rock.
The only derived construct of our noun πετρα (petra) is the adjective πετρωδης (petrodes), which consists of our noun petra and ειδος (eidos), meaning appearance (from the verb ειδω, eido, meaning to see). The adjective petrodes describes not a land strewn with rocks, but rather a land that's so hard that it could be mistaken for a slab of rock. This word occurs an additional 4 times; see full concordance.
A petra is used to build houses in and on (Matthew 7:24, Luke 6:48) or hew sepulchers in (Matthew 27:51, Mark 15:46). It's also used to metaphorize someone's firmness or strength; the Septuagint uses it in 2 Samuel 22:2 in the familiar phrase "The Lord is my petra and my fortress." Paul refers to the Meribah event in 1 Corinthians 10:4, and compares Christ to the petra from which the waters flowed (Exodus 17:6).
Petra denotes a firm foundation and as such it serves as a metaphor for faith in Jesus Christ (see our article on the word πιστις, pistis, meaning faith, for more on this). The masculine counterpart of petra is πετρος (petros), which denotes a wobbly flint that won't supply any footing and can be tossed away at will.
The masculine noun petros could mean rock in Homer's time but in the time of the Bible, it was always used to indicate "a piece or fragment of a rock such as a man might throw," as Zodhiates' Complete Wordstudy Dictionary New Testament explains, "Distinguished from the masculine petros is that petra is a mass of rock while petros is a detached stone or boulder, a stone that might be thrown or easily moved."
In the Bible the word petros does not occur besides the name Peter.
The most remarkable conjunction of these two words petra and petros is in the famous scene of Matthew 16:13-20. In Matthew 16:18 Jesus asks the disciples what they think of him. The men rattle off a list of heroes but only Peter submits that Jesus is the Son of the Living God. Jesus responds by saying that he couldn't have obtained that insight from any human teacher, or even have figured it out by himself, but that it was given to him by God.
And then Jesus says to Peter: You are petros (a small wobbly and easily movable stone), but on that petra (the unmovable faith that is not from man but from God) I'm going to build my church.