• and
  [connects two or more single words]
• together with
  [in a series of words where it appears before the second word so that the first word will agree with the singular verb]

  καὶ ἀνέβη Μωυσῆς καὶ Ἀαρὼν καὶ Ναδὰβ καὶ Ἀβιοὺδ
  Moses went up together with Aaron and Nadab and Abiou (Ex 24:9)

• including, as well as (See Acts 4:5-6 where specific individuals in v.6 are added to the general list in v.5)

δέκα καὶ ὀκτώ (Luke 13:16)
10 and 8 = 18

Πέτρος καὶ οἱ ἀπόστολοι (Acts 5:29)
Peter and the apostles (does not exclude Peter from being an apostle)

ὅσα προσεύχεσθε καὶ αἰτεῖσθε (Mark 11:24)
literally: whatever you pray and ask
but means: whatever you ask in prayer

ἐξίσταντο ... ἐπὶ τῇ συνέσει καὶ ταῖς ἀποκρίσεσιν αὐτοῦ (Luke 2:47)
literally: they were amazed at his intelligence and answers
but means: they were amazed at his intelligent answers

ἐγὼ γὰρ δώσω ὑμῖν στόμα καὶ σοφίαν (Luke 21:15)
literally: I will give you mouth and wisdom
but means: I will give you wise utterance

τροφῆς καὶ εὐφροσύνης (Acts 14:17)
literally: food and joy
but means: joy in your food

περὶ ἐλπίδος καὶ ἀναστάσεως (Acts 23:6)
literally: concerning hope and resurrection
but means: concerning the hope of resurrection

Ἠσαΐας δὲ ἀποτολμᾷ καὶ λέγει (Rom 10:20)
Isaiah is bold and he says
Meaning: Isaiah is bold to say

χαίρων καὶ βλέπων (Col 2:5)
rejoicing and seeing
Meaning: I rejoice to see

• Regarding time: when

  ἤγγικεν ἡ ὥρα καὶ ... παραδίδοται (Matt 26:45)
  the time has come when he is to be given up

  ἦν δὲ ὥρα τρίτη καὶ ἐσταύρωσαν αὐτόν (Mark 15:25)
  it was the third hour when they crucified him

  ἦν τὸ πάσχα ... καὶ ἀνέβη εἰς Ἱεροσόλυμα (Jōhn 2:13)
  it was the Passover when he went into Jerusalem

  Also see: Jer 38:31; Luke 19:43; 23:44; Jōhn 4:35; 7:33; Acts 5:7; Heb 8:8.

• Introducing apodosis (if-result clause): and then
  See Luke 2:21; 7:12; Acts 1:10
• Connecting Positive and Negative clauses: and

  οὔτε ἄντλημα ἔχεις καὶ τὸ φρέαρ ἐστὶν βαθύ
  you have no bucket and the well is deep (Jōhn 4:11)

• Introduce a result from what precedes: and then, and so

  Δεῦτε ὀπίσω μου, καὶ ποιήσω ὑμᾶς ἁλιεῖς ἀνθρώπων (Matt 4:19)
  Come follow me, then I will make you fishers of men

  εἰπὲ λόγῳ, καὶ ἱαθήσεται ὁ παῖς μου (Matt 8:8)
  Say the word, then my servant will be healed

• Emphasize something noteworthy, surprising, or unexpected: and yet, and in spite of that, nevertheless, but

  οὐχὶ δύο στρουθία ἀσσαρίου πωλεῖται; καὶ ἓν ἐξ αὐτῶν οὐ πεσεῖται ἐπὶ τὴν γῆν (Matt 10:29)
  Are not two sparrows sold for a coin? And yet one of them doesn't fall to the ground!

• To introduce an abrupt question:

  καὶ πόθεν μοι τοῦτο (Luke 1:43)
  how have I deserved this?

  καὶ τίς δύναται σωθῆναι (Mark 10:26)
  who then can be saved?

• To introduce a parenthesis:

  καὶ ἐκωλύθην ἄχρι τοῦ δεῦρο (Rom 1:13)
  but so far I have been prevented

ἔρχεται ὥρα καὶ νῦν ἐστιν (Jōhn 5:25)
the hour is coming, indeed is now

πολλὰ καὶ βαρέα αἰτιώματα (Acts 25:7)
many and serious accusations
means: many serious accusations

Πολλὰ καὶ ἄλλα σημεῖα (Jōhn 20:30)
many and other signs
means: many other signs

τί καὶ ἐλπίζει (Rom 8:24)
why does he still hope?
Also see 1 Cor 15:29

οἳ καὶ ἐκδύσαντες αὐτὸν (Luke 10:30)
who stripped him

μετὰ καὶ Κλήμεντος (Phil 4:3)
literally: with and Clement
Meaning: with Clement

Σαῦλος δέ, ὁ καὶ Παῦλος (Acts 13:9)
Saul who is also Paul

καὶ εἰ κατεμείναμεν ... παρὰ τὸν Ἰορδάνην
if only we had remained ... beyond the Jordan

κατὰ καιρὸν
opportunely, timely, appropriately