there are always gravitational forces, space has structure, you will always fall towards something
think of space curvature better as the requirement of thurst you need from earth to escape the sun
say i want to launch right now, with 1 rocket i can get to certain earth orbit but not other orbit because my thurst isn't powerful enuf
say i want to get beyond the moon in 1 go without orbital acceleration i would need much bigger rocket or else my escape velocity will never be fast enough to escape
same for the sun the next gravitational body, i would need a much much larger rocket to escape sun's gravity in 1 go from earth
this is why the probes had to slingshot so many times or else they will just fall into some orbit around the sun
