When Penny first met Leonard, she only thought as him as a neighbor and a friend and had no romantic feelings for him at first.
She also has issues since other members of her family were pregnant when they got married.
In "The Recombination Hypothesis", Leonard (having broken up with Priya) decided to ask Penny out on a date and envisioned a possible ending of that date.
In his fantasy, things did not go well the second time around, but he decided to go ahead and ask her out anyway, and Penny agreed to go.
When Leonard returned at the beginning of Season 3, he went to see Penny and she greeted him with a passionate kiss which Leonard happily returned.
Leonard gave her a preserved snowflake which she loved and they began going out again.