Hi Katarzyna!
If it is being used in the way I think it is, it means you have done something after being persuaded or encouraged by someone/something. It comes from the phrasal verb "to push someone into doing something"
For example, "After a bit of a push, I have finally signed up to Instagram. My friends and family have been telling me to sign up for ages, and I have finally done it".
I hope this helps!