37-38 weeks pregnant, tightening on area just under the breasts (i don't know what its called) usually at early evening. what could this mean?

Labor prep: Sounds like your body may be getting ready for labor. The same hormone that brings about your contractions (oxytocin) also has a similar, somewhat diluted affect on some of the cells in the breast (myoepithelial: contractile milk duct muscles). While it's hard to say how close labor may be, based on your present symptoms; it sounds like your body may be preparing.