In a democratic country, we expect government to do what benefits its voters. It is not clear to me:
- What is the voting group that demands foreign aid?
- If they want it - why don't they just send their own money instead of taxpayers' money?
In democratic country government must do what benefits its voters.
This doesn't seem like a valid premise. It would be more correct - but still simplified - to say that in a democracy, a government must do what the majority of voters want.
There are many things that do not benefit any voters or the majority of voters directly: the right to asylum, cutting taxes for the super-rich, etc. They are still done for a variety of reasons.
What are the benefits of foreign aid for voters?
There are basically two benefits:
I think the second point should be obvious, so let's focus on the first.
A prominent example is the Marshall plan, which was at least partially meant to prevent the spread of communism (which it did).
In general, foreign aid can improve diplomatic relations with the receiving country, it can be used to (militarily) strengthen allies, to influence their internal policies, to stabilize the country and to improve their economy and infrastructure (thus providing investment and trade opportunities).
See for example this Forbes article which argues along the same line: Foreign Aid: The Good And Bad
If they want it - why don't they just send their own and not taxpayers money?
They do. But this argument doesn't make any sense. You might as well ask why the government builds roads; If you want a road, just build it yourself.