There's a great, very simple, explanation of the theory behind this idea - the £10 note explanation.
A farmhand is given a £10 by his boss for working on the farm. He uses it to pay his rent. His Landlord goes to her hairdresser and uses the £10 note to pay.
The hairdresser takes the £10 note and runs down to the village shop, and buys her shopping. The shopkeeper uses the £10 note to pay the farmer who supplied his eggs.
And the Farmer uses the £10 note to pay the farmhand.
The same ten pound note has been paid to one person, moved through all the others and been used again. Everyone has what they need and no-one is in debt - just from the movement of that one note.
What the vouchers would (theoretically) do is start this chain with 'A man finds a £10 note on the floor - introducing the £10 to the economy from outside. The key is to look at how much work that one note does, and how many individuals and businesses are assisted by it.
The other change to the cycle in introducing the 'new' £10 note is that several of those steps include 'and pay their taxes', including the farmer, who is now making a profit. :-)