To "consider ___ing" means to think carefully about doing something, so that you can try to decide whether you want to do it or not. Before you make a big decision, you "consider ___ing" for a while. For example:
We're considering buying a house.
You would say this when you've started to talk with your husband or wife about buying a house, but you haven't definitely decided whether to buy one yet.
A more casual way to express the same idea is "thinking about ___ing":
I hear you're thinking about going into medicine.