That message means make can't figure out how to build that target (RumPi.o). Do you have a Components/Implementations/RumPi.cpp file? Do all the header files you've listed in the $(HEADERS) variable actually exist? If either of those is not true, then your pattern rule will not match. If your pattern rule doesn't match (and the default rule doesn't match) then make can't figure out how to build the object file.
If you want full details you can run make -d and examine the debug output. You might want to redirect it to a file so you can look at it with less or a text editor since there's a lot of output.
By the way, you should not add the -lwiringPi option to your compile line. Libraries are only used at link time, not compile time.
ETA
Something else you should consider is rewriting your pattern rule so that only the source file is listed as a prerequisite and moving the headers to a separate line:
%.o: Components/Implementations/%.cpp
gcc -c $< -o $@ -lwiringPi
$(OBJECTS): $(HEADERS)
The advantage to this is you'll get a clearer error message if one of the headers is not found. When you use a pattern rule, make will try to match all the patterns it can and if none match it tells you it doesn't know how to build the target. Since there are usually many different ways to build a target, make doesn't show an error for every one that doesn't match.
But if you declare a direct explicit prerequisite relationship between two files, rather than using a pattern that may or may not match, then if there is a missing file make will tell you directly.
ETA2
In your original makefile you had a rule like this:
RumPi: $(OBJECTS)
gcc $(OBJECTS) -o $@ -lwiringPi
but then later you removed it. Why did you take this out? You need this rule to tell make how to link your executable file RumPi.
Also, you shouldn't be using gcc as the compiler/linker for C++ code; gcc is for C, not C++. You should use g++ for C++ code. And it's best to contain this information in variables so it's easy to find and modify (even from the command line if you like). The standard variable names for the C++ compiler is CXX etc.
Your makefile should look something like this:
CXX = g++
CXXFLAGS = -std=c++11
LDLIBS = -lwiringPi
HEADERS = Components/Headers/RumPi.h ./Common.h Components/Headers/Component.h \
Components/Headers/Vehicle.h Components/Headers/Motor.h Components/Headers/Receiver.h \
Components/Headers/DualLED.h Components/Headers/LED.h Components/Headers/RGBLED.h \
Components/Headers/Relay.h
OBJECTS = RumPi.o Vehicle.o Motor.o Receiver.o DualLED.o LED.o RGBLED.o Relay.o
default: RumPi
RumPi: $(OBJECTS)
$(CXX) $(CXXFLAGS) $^ $(LDLIBS) -o $@
%.o: Components/Implementations/%.cpp
$(CXX) $(CXXFLAGS) -c -o $@ $<
$(OBJECTS): $(HEADERS)
clean:
-rm -f $(OBJECTS)
-rm -f RumPi
