There are actually several different images of constellations that appearsappear in Contact at various different times. The most prominent are hethe constellation Lyra, which contains the star Vega from which the alien signal emanates, the constellation of theThe Plough (Big Dipper) and the constellation of Corona Boreallis.
Taken together they appear to be a metaphor for Ellis's search for meaning and contact throughout her life.
The flashback scene during which a young Ellie and her father are watching the Persied Meteor shower which is associated with the ploughPlough (Big Dipper) is one of the most significant. When Ellie's father collapses the ploughshape of the Plough can be scenesceen in spilled popcorn on the floor. In the DVD comentary track Jodie Foster makes a passing reference to it but I no longer have that disc so cannot add more detail.
The computer screens in the VLA controlled room for obvious reasons show many images of Lyra which contains Vega.
It has often been said on various internet pages -for example https://www.reddit.com/r/Astronomy/comments/skaux/hidden_message_in_contact_1997_movie/ - that the constellation Corona Borealis was Carl Sagans favourite constellation because of its apparent resemblance to the shape of a radio telescope. I cannot find a direct quote but this is repeated in many different places on the web. It certainly is the constellation that appears in sand in Ellie's fathers hand.
It's likely significance is that it acts as a metaphor for Ellie's search for meaning and contact in her life, even as an invitation to keep exploring, as in "take my hand I will help you on your way" which is what the aliens are trying to do. That
Taken as a whole, starting with the meteor scene and the plough, she is lost, searching for meaning missing the contact with her father, then receiving the message from Vega in the constellation of Lyra she has a direction in which to seach, which finally leads her to going on the mission in the machine and encountering the apparition of her father who by showing her the grains of sand in his hand suggests a direction in which to keep looking and at the same time offering her the contact with her feelings and ambitions that she has been searching for all along.
All of that said exactly how you interpret thatthe metaphor of the constellations will always be a little bit dependant on the viewer.
You can see a star map showing both Lyra and Corona Borealis here...
https://www.skyatnightmagazine.com/advice/hercules-constellation/