What is Katniss' connection to Peeta?

Answer 1

They went to school together, and Peeta had a crush on her. When they got older, he saw her starving and threw her some bread that he was supposed to feed to the animals.

And then they both went to The Hunger Games together, where he and Katniss became friends.

The only connection they really have is that they're friends and he loves her.
They first met when Katniss was younger. She was out in the rain, looking for food while her family was starving. She was searching through trash cans when she attracted the attention of the baker's wife and son. The "witch of a wife" wife told Katniss to leave. She collapsed by a tree in the yard, unable to walk. Peeta snuck out of the house with bread he had intentionally burned, and tossed it to Katniss.

They later were both reaped for two Hunger Games; the 74th, and the 75th, also known as the Quarter Quell. They started to bond and care for each other immensely, to make an understatement. After the Quarter Quell. Peeta was kidnapped by the Capitol, and brutally tortured. He was recovered, in hopes of raising Katniss' moral, so she could be the face of the rebellion more effectively. After the rebellion was over, Katniss chose to be with Peeta over Gale, and then got married and had two kids.

Answer 2

They first met when Peeta gave Katniss some food, and then everyday since, Peeta would watch her walk home everyday to make sure she was safe. Katniss didn't recognize him when they were called for the games, but soon remembered. Peeta's love for Katniss is probably on hold right now because after the games in the first book, Peeta found out Katniss didn't really love him back, it was just an act for the Capitol cameras. Hope I helped! :D