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:][1]  `I'm off; see you later​.`

According to [this answer,][2] 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,*][2] 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,][3] as well as this [website.][4]  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.


  [1]: http://jisho.org/search/%E8%A1%8C%E3%81%A3%E3%81%A6%E3%81%8F%E3%82%8B
  [2]: https://japanese.stackexchange.com/a/677/22352
  [3]: https://japanese.stackexchange.com/q/676/22352
  [4]: https://www.renshuu.org/grammar/82/%E3%81%A6%E3%81%8F%E3%82%8B