What does "pay its own way" mean?

Pay one's own way: to pay for one's own transportation, entrance fees, tickets, room, board, etc.

I wanted to go to Florida this spring, but my parents say I have to pay my own way.

Yes it means "pay back your investment in a year".

To be honest, as a native speaker at least passingly familiar with basic finance, I'm not sure what it means in this context either.

Possibilities are:

• The product is making enough in sales to cover its per-unit production costs (and distribution and marketing costs?).
• The product has made enough net profit within one year to pay back its intitial development costs.

These are two very different things. Its even quite possible the speaker put it in exactly this imprecise way in order to mislead his audience. When someone is talking money, it is wise to bring all the cynicism you can muster.

“This product will pay its own way in one year" does not mean "This product will pay back your investment in one year".

It means, "This product will pay back its on-going expenses, starting one year from now."

If you buy a car, and the car "pays its way", that would mean the value you get for it makes up for costs of fuel, maintenance, and so on. Its initial cost is another matter.