Dill finds that he must exaggerate the looks and actions of his father, perhaps in order for him to stack up with other fathers with greater real virtues, such as Atticus. In Chapter 4 of To Kill a Mockingbird, Dill describes his father as taller than Atticus (Atticus was quite tall), with a pointed black beard (a mark of distinction or regality). He was also president of L&N Railroad. Dill even claimed to have helped him engineer a while. But Jem didn't buy the story. He told Dill to "Hush," and quickly changed the subject to playtime.
Dill's family life is disjointed to say the least. He is embarrassed and hurt because his parents ship him off each summer, and they apparently spend little time with him while he is living with them in Meridian, Mississippi (his home town in the story). He exaggerates his father's description and occupation in order to impress Jem and Scout, but the Finch children already realize that Dill is quick with a story. Dill was embarrassed when Jem and Scout first asked about his father, and Jem finds it best to avoid the topic. It is likely that Dill does not know his father at all, so he resorts to his familiar storytelling to try and impress Jem and Scout.
Dill must not really know his father. If he does, he is happily covering the truth, which is entirely possible because Dill likes to tell big ones (lies).
Dill does describe his dad as a man with a big black beard who lets him help engineer and actually drive the train for the railroad company. Although, I'm not positive that is chapter 4. Another editor may confirm.
His family situation looks like he is carted around from relative to relative so there must not be real stability in his life. His mother did enter him in a beautiful child contest once and won 5 dollars for it. Dill went to the picture show lots of times on that one... including Dracula. Most of what Dill reports about his parents is to impress Jem and Scout. Other children don't necessarily have that pride in their parents. I think this means Dill is covering something up.
In this chapter, I believe, we are told three things about Dill's father. First, he is taller than their father. Second, he has a pointed black beard. Finally, he is the president of a railroad.
We do not know if any of this is true, but it seems that Jem does not believe the last claim, at least.
To me, this shows that Dill does not really have a very close relationship with his father. He is trying to make up some idealized father. His fantasy father is one who is tall and maybe a bit dangerous looking with an important job. This implies to me that Dill is not satisfied with the way his father is and I assume that is becauses his father does not really pay attention to him.
bullgatortail answers the prompt in the best way