Often the particle "da" is used to denote the use or destination of something:
- Palla/Pallone da calcio (ball for playing soccer/football)
- Vestito da sposa (suit for a bride)
- Tabacco da fiuto (tobacco to be sniffed)
...and many more.
In this phrase, "molte cose da fare", the particle da suggests that the cose still are to be done, they are destined to be carried out.
This preposition is used also with other verbs:
- Cose da comprare (things that can or should be purchased)
- Cose da prendere (things that can or should be taken)
- Cose da sapere (things that one should know)
On the other hand, sometimes the preposition "a" is used the same as in French, like in
- Vuoto a perdere (one-way container/bottle; the bottle will be lost [perdere])
- Apertura a strappo (tear opening)
but this usage is more found in ready-made periphrases than in constructions a speaker elaborates. Sometimes it is easy to understand why "da" is preferred, for example "bastone da passeggio" (walking stick) is not referred to as "bastone a passeggio", which would mean that the stick is taking a walk by itself (maybe accompanied by its owner!).