Spoiler text below. Highlight to read.

Go is played on a 19x19 board with letters horizontally (skipping the letter I) and numbers vertically. The bottom left square is thus A1 and the top right square is T19 (not S19, because again, I is skipped.)

The first move for black is R16. This move is so that White's 3 stones will find it difficult to escape. White cannot play at S15, otherwise black will play T18 and make a connect and die and a second eye. So in order to try to escape white must play S16 instead. Black pushes at S15 and White bridges under at T15. Black throws-in at T16. White cannot take because then Black can force a direct ko.

So instead, white bends and makes it impossible for black to approach directly by playing T18. Now, black must push at M16. If White does not block at L16 then black can escape and make life elsewhere. So White blocks. Black will cut at L17. White gives atari at K17, because giving atari the other way will cause white to have two weak groups, which black will be able to exploit and escape. Black descends to L18. White blocks at K18. Black pushes at P17, threatening to make an eye out of the P18 stone. White responds by connecting at O18. Black plays M18, which is again sente on White's P18 group. White responds at N18.

The entire entire last paragraph was so that Black could play P19 in sente. White must respond by giving atari to black's group, either at M19 or L19. Then black captures the stone at T15.

Now black is alive. However, it's a special kind of life called Chosei. If White throws in at Q19 then black must play T19. White captures at R19 and black captures back at S19 and the cycle restarts. Black can eventually add another move to remove the indefinite ko threats.