This grammar point is a combination of the conjunction particle て, and the verb 来（く）る ‘to come’. To use this grammar point, you will need to attach て to any verb, and then follow it with くる. This nuance is usually that ‘(A) happened, and then came’, or ‘will happen, and then come’. In other words, it will depend on whether くる is in present, or past tense.

• 今日（きょう）も宿題（しゅくだい）を持（も）ってくるのを忘（わす）れた。
  I forgot to bring my homework today too. (To ‘come with’ homework was forgotten)
• パパ〜、じゃが芋（いも）を買（か）ってきたよ！
  Dad, I bought the potatoes. (Bought and ‘came with’)

てくる can be used when representing time, or when representing a physical place. When representing a physical place, it is more likely that the kanji structure, 来（く）る will be used. However, this is not a set rule, and depends on the writer.
When used in relation to time, the nuance is usually that something has already come to pass, or will start to happen from now.

• 最近（さいきん）、日本語（にほんご）が上手（うま）くなってきた感（かん）じがする。
  Recently I feel like I have come to be better at Japanese. (Very similar to ‘gotten’ in English)

This is the opposite of ていく, which indicates that something will change from the way that it is now, or will continue progressing in a certain way.