As shown in the season 5 of Game of Thrones, Stannis' daughter was burned alive by Melisandre, the Red Woman.
Why did Stannis not try to save her? He seemed to really love her.
Is ambition and power more important to him than love?
This is difficult to answer since:
This incident never happened in the books.
We are never privy to Stannis' inner thoughts on the matter.
Looking back at his history there are two possible motivations that would have lead him to prioritize the war over his daughter's life:
Ambition for power. Stannis has never made it a secret that he desires the Iron Throne and he oft repeats that it is "owed" him. So perhaps he values the Iron Throne and all the rights that were denied him over his daughter.
To serve the greater good. Stannis is also a (cautious) believer of the war between R'hllor and the Great Other. He believes that defeating the Great Other is his greatest mission, and being the king of Westeros is only a stepping stone towards that great goal. He has also been lead by Melisandre to believe that sacrificing his daughter is the only way for him to move forward in this war. So perhaps he sacrificed his love for his daughter in order to defeat the Great Other, much in the way that Azor Ahai (who some believe he is an incarnation of) sacrificed the life of his beloved wife Nissa Nissa to forge Lightbringer.
In my mind, the second is the most convincing.
In the book, he orders the burning of couple of his own men at the behest of Melisandre. I believe this is what they replaced with his daughter in the TV series.
The reason he does it in the books and as far as I can make out, in the TV series, is as a sacrifice to R'hllor for a favorable weather so that he can continue his march on Winterfell. The unrelenting snow and cold weather was taking a toll on his army. He lost men and horses and the snow was slowing his progress.
To Stannis, the Iron Throne is his destiny and he will allow nothing to stand in his way so probably he would have considered it acceptable sacrifice.
Personal view point below: This is shoddy script writing done just for shock value. There is no real justification for Stannis to sacrifice his own daughter. In the books when they find one of King Roberts bastard sons, he was extremely reluctant to allow Melisandre to sacrifice him. As you noticed this makes it look like he was willing to sacrifice ANYTHING for the sake of attaining power. Also, in the Books, Stannis is more interested in the power that Melisandre wields through the lord of light. He is not shown to be overzealous in the praise of the God or the beliefs of Melisandre.