Historical present

Historical present, also known as narrative or dramatic present, is the use of the present tense in narrating past events. This is often done to make the account more vivid or dramatic. It is common in koine Greek and occurs frequently in the Gospels of Mark and John. When translated into English, however, these passages are typically rendered in the simple past tense.

The use of the historical present is common in verbs of speech, motion or for transitions, when something new is coming on to the scene.

Examples
John 1:29: Τῇ ἐπαύριον βλέπει τὸν Ἰησοῦν ἐρχόμενον πρὸς αὐτὸν καὶ λέγει· ἴδε ὁ ἀμνὸς τοῦ θεοῦ ὁ αἴρων τὴν ἁμαρτίαν τοῦ κόσμου. (Τhe next day he (John) sees Jesus coming to him and he says: behold the Lamb of God who takes away the sins of the world.)