How to speak Brainfuck: for beginners
First of all, let's not beat around the bush. Clearly your filenames should be Brainfuck.hpp and Brainfuck.cpp. Let's not be shy. Now for the real reviews:

Input

std::string currentLine = " "; // do not start empty

while (currentLine.length() != 0) // escape input by an empty line
{
    std::getline(std::cin, currentLine);
    userInput.push_back(currentLine);
}


This is bad. getline() could fail - and you'd expect it to fail when the input runs out. But you're not checking the result of getline(), so you end up writing an extra string onto your vector. The correct approach would be:

for (std::string currentLine; std::getline(std::cin, currentLine); ) {
    userInput.push_back(currentLine);
}


This ensures that you get the correct strings in your userInput.

Looping

Since this is tagged C++11, you definitely want to use a range-for expression to do your loop. It's less code and clearer:

for (const std::string&amp; str : userInput) {
    std::cout &lt;&lt; modifyString(str) &lt;&lt; std::endl &lt;&lt; std::endl;
}


Know what's in the standard

Your modifyChar() function's job is to pick some character (either + or -) and return a string with that character next times, followed by a period. You do not need a loop for this. There is a constructor for std::string that takes a count and a character and constructs a string with that character that many times.

Thus:

std::string modifyChar(char input, int carry)
{
    int next = input - carry;
    std::string output = (next &gt; 0) ? std::string(next, '+')
                                    : std::string(-next, '-');
    return output + '.';
}


And same comment about looping again for modifyString. Though additionally you should take input by reference-to-const, to avoid a completely unnecessary copy:

std::string modifyString(std::string const&amp; input)
{
    std::string output;
    int traveller = 0;
    for (char c : input)
    {
        output += modifyChar(c, traveller);
        traveller = c;
    }
    return output;
}