As Richard says, the first product will be overdrafts which have been described in some more detail here
Monzo are asking for feedback about how the overdrafts should work here
it seems that Monzo's business model is reliant on the fees from overdrafts, as Tom has specifically said that
The idea of one bank providing every service (mortgages, credit cards, p2p lending etc.) is no longer credible
Since Monzo will have an open API, the hope is that developers will be integrations which will create an ecosystem of value added services which is partly what will set Monzo apart from competitors. Tom's described some of those integrations in this video.
The challenge that competitors like Atom have is that they are building services on top of legacy banking infrastructure with all of the limitations that result (Tom also talks about those in the above video).
Starling seems like the most similar company to Monzo, Tom & a few employees actually left Starling to found Monzo but they're much more secretive so we don't know as much about their product.
In any case, it's very early days for all of these companies.
I'd recommend checking out the article that I've posted in the above thread from Bloomberg, as it gives a really good overview of the current state of the entire ecosystem of fintech banks in the UK.