NAT (Network Address Translation) is a technique for allowing multiple computers to share a single IP address. It's advantageous for a couple of different reasons: it allows us to change your IP address without forcing you to reconnect, and it makes it impossible to correlate a single external IP address with a single VPN user.
VPNme offers a few different NAT modes that let you control how your publicly-visible IP address is chosen. You can find these settings in your VPNme account. Make sure your tunnel mode is set to NAT.
Single assigns you a single IP address at random for the duration of your session. It may be shared with other users, but won't change while you're connected. This is the default.
Per-destination uses a different IP address for each server you connect to. So, website A will see you as X.X.X.X and website B will see you as X.X.X.Y, etc for the duration of your session. This is a good compromise between Single and Random modes.
Random chooses a different IP address for each connection you open. A single website will see you first as X.X.X.X, then X.X.X.Y, etc. This is awesome, but not all websites are able to handle this. Specifically, if you find that you're unable to log into a website, or it keeps telling you your session has expired, Random mode might be to blame.
As a bonus, you can change your IP address any time you want by clicking Randomize Now. This won't do much if you're using Random mode, but in the other two modes, it will cause any new connections to have a different IP without breaking existing connections.