Hello Amy,
The two sentences basically mean the same thing:
1. I came in and kindled a fire in the stove.
2. I came in and lit the stove.
To kindle a fire = to light a fire.
The second sentence is just a shorter, simpler version of the first sentence. It is understood that you lit a fire, even though you leave out the "fire" part of the phrase.
Also, to my ear, the word "kindle" is not used very much. The more common thing to say is "I lit a fire (in the stove)".
Hope this helps.