At 15 people, you can rely on 'tribal knowledge', where there is enough interaction between individuals that everyone is on the same page on most key points (company mission, coding standards, release processes, etc.)
As you grow, that stops being the case; to echo what @Peroni and @sloaken said - a good first step is good documentation and clear, repeatable and where possible automated processes. A second, related challenge is company culture - as you grow and interactions between each & every individual become less & less possible, getting everyone aligned on what it means to work at your company (and how to achieve company goals) is harder. You'll need to make a conscious effort to maintain that (see below).
The core team will need to start delegating more, which can be a hard if you're not used to it (some may also want to remain ICs), and will change the shape of your organisation. This is particularly hard to do gradually, as you'll need to work out the right point at which to transition different areas of the business. This comes with the risk of silos developing - a good way to work around that at mid-size is to continue arranging teams by project, but make sure that there are both opportunities to gather across functions (e.g. dev, qa, project management etc.) and more widely (e.g. company events, social events etc.). The main thing here is making sure people talk to each other, exchange information, getting good at collaborating with each other and know who to reach out to in case of issue. Again, you are going to have to dedicate time to this which will seem strange coming from 15 people (but will pay off handsomely in increased efficiency).
There are many good other points in this thread (on hiring experienced people even though they cost more, the importance of good hiring, clear ownership, us vs them), but a last one is the need more generally for the leadership team to adapt. They will have less visibility and control; the company will become less efficient which might be frustrating (it will still be able to do more overall); changes of direction will become harder and slower. This applies to all 15 people working there now, but particularly for the founders/leaders. Having some thoughts on how to handle this ahead of time (established reporting structures, clear goals and reporting metrics) will help minimise growing pains. It's always easier to say this than to do of course.
Source: did something similar a couple of times (4->25 people, 600->1000 people).