The above is a common German phrase that appears a bit odd in English, in that it seems to have the prepositions "on" and "to" in it, but that's not the case. On its own, the verb zukommen means "to belong to" or "to be assigned to," but when you add the preposition auf, together with a direct object such as einen, mich, dich, sie, ihn, uns, etc., its meaning changes: 

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Ich weiß ja noch nicht, was auf mich zukommen würde.

I don't know yet what would lie ahead of me.

Caption 83, 18 Miss-Kandidatinnen - beim Friseur

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Wir wussten, was auf uns zukommt.

We knew what to expect.

Caption 55, Fußball - U21-Nationalmannschaft

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...weil wir eben zu viele Einflüsse haben, die auf uns zukommen.

...because we just have too many influences that are reaching us.

Caption 29, Gamification - Wie Spielen den Alltag interessanter macht

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Wie wenn Störtebeker eine Hanse-Kogge auf sich zukommen sah.

Like when Störtebeker saw a Hanseatic ship approaching him.

Caption 89, Großstadtrevier - St. Pauli rettet HSV

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Die Koggen, die du heute Abend auf dich zukommen siehst...

The ships that you'll see coming toward you tonight...

Caption 92, Großstadtrevier - St. Pauli rettet HSV

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Damit war eigentlich nur gemeint, ob euch klar war, wie viel da auf euch zukommt.

I actually just meant whether it was clear in your mind how much there is in store for you.

Caption 20, Luxuslärm - Interview

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As you see above, depending upon the context, auf [einen] zukommen is variously translated as "to be expecting someone or something," "to be reaching someone or something," "to be approaching someone or something," "to be coming toward someone or something," and "to be in store for someone or something." 

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Further Learning
Look at the examples above on Yabla German to get a better grasp of the contexts in which auf einen zukommen is used so that you can better understand its meaning and learn how to integrate the phrase into your own vocabulary.

When the Old Testament was translated from clerical Latin into the common spoken languages in the 16th century, it had a profound effect on European spoken languages and literature. Many of the phrases derived from this work are so common that people are often not even aware of the source. Here are some examples of phrases with a scriptural background that German and English languages use in everyday speech.

BANNER PLACEHOLDER

Und neunzehnhundertfünfundneunzig

And in nineteen ninety-five

hatte ich dann die erste Ausstellung zu diesem Thema ...

I then had the first exhibition on this theme ...

„Es werde Licht“.

"Let there be light."

Captions 17-18, Malerei - Benno Treiber

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Essen kann er auch in Ruh'. Vater drückt ein Auge zu.

He can eat in peace. Father turns a blind eye.

Caption 4, Der Struwwelpeter - Ausschnitte

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Selbstverständlich, wie auf meinen eigenen Augapfel.

Of course, like the apple of my eye.

Caption 11, Abenteuer und Sport - Fallschirmspringen

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Hochmut kommt vor dem Fall.

Pride comes before the fall. [Pride goes before a fall.]

Caption 24, Eva erklärt - Sprichwörter

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Worte zu Asche und Staub zu Staub

Words to ashes and dust to dust

Caption 46, Luxuslärm - Interview

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The above is a play on the usual saying "Ashes to ashes, dust to dust."

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Further Learning
Be sure and see the latest Yabla video Eva erklärt - Sprichwörter for a selection of more German phrases on Yabla German.