According to the dictionary definition, a "soft spot" means a particularly strong feeling or tenderness or fondness for someone/something. In the sentence that you mentioned, the person who is speaking seems to be particularly fond of you.
Maybe due to this soft spot, they are more affectionate or kind to you than they are to others. Or perhaps this soft spot causes them to go out of their way to help you, protect you, or make you happy. This could be for a number of reasons.
For example, some grandparents have a soft spot for their grandchildren, which leads them to be extra kind, affectionate, and giving towards them. A friend may have a soft spot for you which makes her want to protect you and be extra kind to you. Alternately, a person can have a soft spot for chocolate, which makes them break their diet and give in to the temptation of eating chocolate each time.
The exact context depends on who said this sentence to you, and how they act in accordance to their soft spot.
Hope this helps!