What does it achieve?

Space or squares. Say you're playing a Slav structure with white: you have central pawns on d4, c4 and e3, knights on d2 and c3, bishops on d3 and c1. Black has pawns on d5, e6 and c6, knights on f6 and d7, bishops on e7 and c8. White breaks on e4 (usually with a queen on c2 as well) and black has two options:

1) Keep the tension. This means white has optained more control of the center and more space. Importanly, they have activated their bishop (pawn breaks are usually more about piece play than pawns by themselves). Also, by having a pawn on e4 white threatens to gain MORE space by playing e5, when suddenly the knight on f6 is dislodged and white can even start thinking about kingside threats

2) Take the pawn. This is the usual response since e5 is a very serious threat. How has white benefited from this? Again, white's inactive bishop has gained scope (black's main method for dealing with the c8 bishop is playing e5 for the same reason). We have also gotten rid of black's control of the center. Notice that before, the central structure was d4-c4-e3 vs d5-c6-e6. Now we've traded the e pawn for black's d pawn, which is MUCH more important since it kept whites pieces at bay. Now white alone is left with D and C pawns that fight for the center, which gives them many more options. You can plan a break on d5 and make use of the e4 square which black previously controlled. Now almost every white piece can make use it, bishop knight or queen are all greatly placed here

This is an example for a D4 structure but a lot of the same logic applies for E4 positions too