It's acrylic. Not as rough as wool, not as soft as cashmere.
I have found that specifically with red heart, it's a little rough feeling while crocheting (or knitting), but after the first wash, it is soft.
My daughter as 3 baby blankets that she has used since an infant, made of red heart and I make Baby Blanket Bouquets out of acrylic yarn.
Sorry, this reply is so long, but it's difficult to explain "feel" over the keyboard since everyone's sense of touch is different.
Acrylic (and cotton) is the most broadly used yarn fiber. You will find many chain store sweaters are made from acrylic or at least acrylic blended with other fibers.