Scrum by-the-book assumes that you release at the end of iteration, then you demo the product to a client. "Release" and "demo" of course may mean different things depending on a product you build, e.g. back office app for big corporation versus an app directly addressed to end-users.
Most Scrum teams try to release at the end of timebox as it gives them more freedom in terms of how the work is done within iteration, e.g. they can start everything at the beginning of a sprint and finish stories only as the sprint end approaches.
However, if you want to release more frequently, which I would personally encourage, feel free to do this, no matter what is the typical practice or what books says. Scrum, as any other method, is not a religion and shouldn't be treated dogmatic.
You might want to introduce (more) frequent releases since:
- They shorten feedback loops--you learn what you did right, what you did wrong, and what should be changed sooner--so you can act on this feedback improving further work faster.
- It also means that you need to automate most, in not the whole, process so you get closer to continuous integration.
- Another thing is it encourages smaller batches of work, which usually is safer way to increment a product, as the smaller the change the smaller the odds that something is going to blow up.
By the way, there are methods that are decoupling planning, release and retrospective cycles. In this case we are talking about cadence. Planning cadence doesn't have to be the same as release cadence or retro cadence is. It's just Scrum that made them so. Read more about cadence versus iteration here.
In general, change to frequent releases affects the team as the tools you use usually have to evolve. You can spend a couple of hours to release a product if you're doing it bi-weekly. If you're doing it every single day, you can't. The good thing is that you may make this transition evolutionary, shortening release cycle step by step, e.g. from bi-weekly to weekly, and looking for pain points and addressing them.