Great question!
行ってくる、or more commonly 行ってきます is actually a really common phrase. The most common usage is when individuals leave their home, but I have (on rare occasion) heard it used when people leave a gathering to go somewhere else. (i.e. party to work) If you look at the translation on jisho.org, you will find the following definition: I'm off; see you later.
According to this answer, we find that 行ってきます has an implication of going, then coming back. This is why you see it most commonly used when an individual leaves home for school/work.
行きます by contrast is simply translated as I'm going.
I want to make a note here: 行ってきます may seem to be related to the baseーて＋くる grammar structure. Since the くる in 行ってきます is actually implying motion, it is not related. Baseーて＋くる means: came/got to be I personally understand it as started to (verb), but that translation has some issues. If you're interested in learning about the Baseーて＋くる grammar, take a look at this question, as well as this website. I suggest that you take some time to study it when you get the chance.
Back on topic-- In short:
行ってきます
Literally: I go and come back.
In natural English: I'm off, see you later!
Finally:
行きます
Literally: I'm going.
In natural English: I'm going.
