Recursion is a little easier to understand if you use goto instead of functions. Functions are a high level concept in the C language (and most other languages) but it gets compiled down to (essentially) the older goto style of programming.

Most modern languages don't even have goto support, since functions are generally more reliable, however as a programmer you should be aware what's going on under the hood. Here's your code rewritten to use goto (I also generally rewrote the whole thing to be a bit easier to grok):

int main(void)
{
    int height = get_int("Height: ");
    int row = 1;
    int col = 0;

draw:
    if (row > height)
    {
        goto end;
    }

    if (col < row)
    {
        printf("#");
        col++;
        goto draw;
    }
    
    // Move to the next row
    printf("\n");
    row++;
    col = 0;
    goto draw;

end:
    return 0;
}