Good quality strength training will overload the muscle and literally tear little holes in it. That's what heals up stronger in the rest day - and that's why the rest day is important.
If your programme isn't doing that to your muscles, there's no need to rest it. Eg some DVDs will include something like 20 side lunges performed to music. Since you're doing these at a low intensity and not challenging yourself till failure, it's fine to keep doing them day after day. You'll build some muscular endurance, and cardiovascular strength.
Typically, you want to rest your muscles if you've worked them to the point where you do max 15 reps to where you can't lift any more with good form.
Deb, in New Zealand