Nowadays Japanese celebrate New Year like Western in 1/1, but in old days, they used lunar calendar... Well, the new year was in this time line (January-February) too.
In New Year day, Japanese have a custom kakizome- They write some words as their wish for a new year like Peace, Courage... as their first writing in the year.
Sesshoumaru was teaching Rin to write the word "Heart".
You can see more calendar page at Moonlight Flower: [link]
Lol sorry for a moment there I thought he was drawing a smiley face. I didn't notice the other stroke on the left side until you said it was heart. xD But beautiful none the less.<3 I love it